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Session I | Session II
| Session III
| Session IV
So Phil, letís start off by asking, at what stage did you become interested in science? Could you tell us
about some formative influences?
I canít remember a time when I wasnít interested in science. We lived in a house where my father was a
scientist and my grandfather had been a kind of scientist, he was a teacher of mathematics. And the house was full of books
and I was just fascinated by the books. There was a four-volume geology book and a three-volume book about natural history.
I donít remember who they were, but what I do remember is that the minions expressed they were terribly old fashioned and now
are all obsolete, but they fascinated me. They had a picture of this pile of clay which you squeezed and mountains came up,
and things like that. No, I canít remember when I wasnít.
If I could interject something, one of the really big influences in my life is very simple. If you remember Shawís
Preface to Pygmalion, he says, every man who amounts to anything turns out to have a strong woman for a mother, and I had a
strong woman for a mother, although, as far as I remember neither parent ever laid a hand on me. I was scared to death not
to achieve adequately, and that was very effective in directing my efforts at least as far as schoolwork was concerned.
Essentially the Andersons and particularly the Osborne, always got Aís and did not intend to be the one who got the first B.
So this went back to my uncle who had been a Rhodes scholar and before him was my grandfather who was a professor of
mathematics in a small college. So achievement was assumed rather than enforced. The [???] I suspect was a little bit like
men early in history. So I canít remember when I wasnít interested in science.
My father, of course encouraged me. He built up for me a chemistry set full of substances which we would no longer be
allowed to have in the home, from which I tried to make fireworks unsuccessfully, things like that. I generated hydrogen in
the basement with it and fortunately didnít blow myself up. And he encouraged me to collect butterflies and to identify
plants, things like that. So there was some encouragement, but I didnít need much.
Do you feel that the science education that you had in school helped you towards developing your interest in
Well, I canít really quite ask, ďWhat science education?Ē but in fact there was at least one rather good
teacher. My school of course was the University High School, which was a very, very good school not because it was an
experimental, which it became later, but because it was an absolutely traditional school that was taught by better teachers,
by university quality teachers instead of conventional teachers. And the practice teachers, kids from the education
department, couldnít really ruin what their professors did. So we tended to learn pretty well and we were very competitive
because there were special admissions, not very difficult, but [???] was admissions requirements for the school.
At the grade school I think the main thing was resistance to whatever they did to us, and when I got to high school
things were very different. I had a wonderful math teacher who was really great, and a very sympathetic biology teacher.
There was a famous physics teacher who was a state-award-winning teacher but who was terrible. He was totally qualitative
and turned me off to physics entirely and I disliked physics, I went to Harvard intending to be in mathematics or chemistry.
I said earlier, whatís important in peopleís lives is really the group that they socialize in, their group of peers.
There was one group, I remember one particular group of peers, a group of five of us at one time, one of us called it The
Five in some pejorative of sense or whatever. We werenít. We were five friends that hung around together. Three of us were
from Uni High, two of us the local high school, Urbana High, but we were clearly probably the brightest kids in each of the
two schools, and somehow we congealed around a girl who was really a mascot it was her mother that was important because her
family had the only, probably the only really good hi-fi in all over Urbana, Illinois, we tried to learn classical music from
the public broadcasts, which were just awful in those days. Weíd go there and listen to records and weíd socialize together
and we had a little string quartet, we organized with the sister of one of the guys. And we all became scientists in one
field or another. Philip Thompson I believe was one of the real pioneers in meteorology. He worked with Tom von Neumann.
He suffered from alcoholism later on. The others were fairly successful in their own fields.
What was it like to be at home? What was the nature of your interaction with your parents?
Really quite good. I was kind of precocious. I was a little younger than some of my classmates, but I had
a very fine setup, a second social group that was important was something called the Saturday Hikers. The University of
Illinois has a really unique group of professors who went out every Saturday, rain or shine or snow. They went out into the
countryside which you wouldnít believe there was near Urbana, Illinois but there was then(and they would find pastures or
woods or wherever and they set up their softball diamonds and play some baseball and have a campfire. They had collected a
set of equipment, coffee pots, jugs for water, and so on. And this group was, at the time I was growing up, was really the
most powerful men on the local campus, the head of the Classics Department, the head of Physical Chemistry, the Provost named
Griffith. The head of Political Science, etc. And there was a ladies adjunct that often went out on Sundays, and of course
the kids were not allowed on Saturdays, only on Sundays. And I would sit back in the corner and listen to them talk around
the campfire and get some idea of what university politics was like, or I would sit very quietly in the backseat and listen
to the discussion. When we vacationed with this group, spent three summers in the Tetons, and I remember we met some of them
in Northern Italy one year when we went to England and we traveled around and saw The Last Supper and other places. So that
was an important part of growing up. It made me used to being around very, very bright people.
One of the memories of the Saturday Hikers of course was, Wheeler Loomis, who was the famous, well known head of the Physics
Department. He started with a moderate-Middle-Western-Big-Ten type department of aging professors who didnít do quantum
mechanics. He made it into a leading department. Then he just basically took any graduate students Fermi had and hired
them. And then when he realized he couldnít hold onto the particle physicists, instead he hired Seitz and Bardeen, and that
was a pretty good move too. He was a very savvy, intelligent man. He told my parents I damn well had better take first year
physics because I could never replace it. Thatís what got me into physics.
Actually, before we get to Harvard, are there aspects of sort of having grown up in a Nirvana, to sort of
put it in sort of somewhat stereotypical concept, small college town in the Midwest that you feel has had a formative
influence on how youíve [???]
Well, just that it had Uni High. Uni High was a very good high school and this group of very bright kids.
I mean I can talk about the three of us from Uni High actually there were three scholarship winners in my year.
Can you mention their names actually?
Wendell Lehmann, who is here in Princeton as a matter of fact. He is one of the founders of Princeton
Instruments Company, along with Bob Dicke, and heís the one who took the millions of dollars that he earned and quit, retired
tooÖ you probably know him and know his wife. He retired to play golf and enjoy himself in Princeton. Then another was
Pierre Noyes, who is notorious if you ever have been at Stanford because heís about half completely wacky and half a very
bright guy. I roomed with him in college, so I know him very well. He was always in some ways a support and in some ways a
terrible problem. He made a big thing out of being a radical. That was his only recourse. He didnít have the personality
that attracted people, so instead he would [???]. And eventually he grew into radicalism. I donít think he was to begin
with, but he gradually grew into it and became notorious for suing the government about the death penalty and various other
things. Itís not that he wasnít bright in many cases, but he talked much more radical than he actually was. He never
actually belonged to the Communist party, but talked as though he did.
Before we move onto your period at Harvard, perhaps I could ask you one last question about your childhood.
Youíve often said that going on sabbatical with your parents made a big difference in your view of the world. Could you
comment a little bit on that?
Well, yes. It was fun. It was great because I was exactly the right age when I saw a lot of things.
How old were you?
I appreciated a lot of things. At least more than what I would have been expected to, although I didnít
have some kind of artistic epiphany. But I got to know Perpendicular from Early English and things like that. I got to know
the geography of Europe very well, visited the Paris Exposition. Drove all the way to Sophia, so I learned about Eastern
Europe, what the difference between Eastern Europe and England was.
Your sabbatical was based in England?
Nowhere in particular. My father spent a couple of months in London visiting Kew Gardens, visiting various
experimental stations nearby. But he was visiting all kinds of places all over England and the continent.
So did you go to school that year?
No, I didnít go to school at all, at least in the spring semester. I had skipped a year the previous year
because I had taken this sub-Freshman skipping program at Uni High. And then the year after that they simply gave me some
class work to do for my second semester. They were very tolerant. I passed some kind of set of exams when I got back. So I
skipped basically a year and a half of school. And I didnít miss anything.
The other thing which was very important to my political orientation and understanding because my parents were very
conscious about it, we talked to a lot of people in Holland and in particularly Germany, people who were still speaking out
to a certain extent about the regime, and I was reading about the interment of Jews very much. So I was overly conscious of
it. I never understood how anyone who was living through that period could not have been conscious of what the Holocaust was
about. Some pretend that they were not conscious and I canít forgive that.
So moving on to your coming to Harvard, describe a little bit what it was like for you to reach there?
Miserable. Well, I was sixteen. I arrived at Harvard at sixteen. Most of my classmates were 18 of
course, and most of the great majority of them were from Eastern Prep Schools. Only about 15% were kind of in the club
system and social, real social. So that was the problem. Most all of us who went to Harvard, 80% of the students ignored
the club system. The clubs were very proud of themselves, but they didnít control the student body. But the Eastern pep
school system did control the student body, and we were the first generation, first in the sense of students who came in on
the national scholarship system which had been established only five years before. We were the first generation of kids to
go strictly need-blind to the major Eastern schools, and I had a need-blind scholarship. They figured what my parents could
afford, by scraping, about $500 dollars a year, the rest was paid, which wasnít that much. The rest was paid by scholarship.
So I wasnít poor, that was not serious. We were in the kind of living quarters suites that were reserved for the kids from
South Boston who came on scholarships. I was not really needy, was just socially incredibly naÔve and young. You know,
there others in the same position.
So for the first year I was feeling pretty lonely. I grew up between that year and the next, and the next two years I
had a wonderful time. Not as great a time as I had in graduate school, but I was mature enough to really relax a little bit.
The first year I took many, too many courses. That was Wheelerís administration. I would take five courses my first year
and then we would coast the rest of the time. That was a terrible mistake coming from the Middle West. I had never learned
to study. I had never learned to take notes from my reading. Boy, we had a real history course, it was not high school
history. That was hard. I just barely scraped by with an A-. That scared me to death that I was going to get a B in that.
I didnít work on French, and I did get a couple of Bs. In the end I think my transcript reads eight A pluses, two A minuses,
and the rest Bs. It was very bimodal.
During this first year when you said you felt somewhat under siege. What were the sorts of things that
allowed you to keep in touch with your parents?
Well you know, I just found physics and math very easy. I had good math training, and physics was just
well taught. So after a couple of sessions of worrying about I was catching on and understanding it, it suddenly became very
easy. So I relaxed in physics and math and worked on the other courses. Of course that first course in physics was so
beautifully taught that really was my fate was sealed from that point on. I was not thinking of physics at this point.
Who taught the course?
Wendell Furry. He was a wonderful teacher. Everything Jeremy Bernstein says in his autobiography was
right. That was really kind of a tragic loss. He was destroyed by the simultaneous arrival of the Un-American Activities
Committee and of Schwinger, and I think that they were twin blows. I mean Schwinger was just a force of nature and you
couldnít hope to compete with it, and Wendell tried to. At the same time he was having all this trouble with the Un-American
Activities Committee, totally unjustified, disastrous for him.
What kind of peer group did you form?
Well, as an undergraduate I was thinking about it, there was basically no peer group. My peers were a few
pickup friends and acquaintances, and Pierre and Pierreís roommate, and a few other guys gradually in the course of a year.
The other peer group was the bright students in physics. We were all working together. Bob Houston, Tom Kuhn was one of
them, Bob Houston, myself, Pierre, a few others. But it turned out we all ended up with summa cum laudes, almost half of the
class that took that physics course ended up with summa cum laudes at the end of the three years, which was all we had. And
they thought it was grade inflation, but it wasnít. It was Tom Kuhn, and Bob Houston was brighter than Tom Kuhn. Henry
Chauncey said it was the brightest class he had probably seen in his life. I think we all did pretty well.
So this is on sort of on the eve of the war as well as in physics at a time when tremendous sort of progress
in quantum mechanics had come about. How much of this got through to you?
Well my family was very politically active. My mother was very active in the local Committee to support
the Allies, whatever that was, an interventionists committee, League of Women Voters. All of the Saturday Hikers were
interventionist and very politically active. So I knew about the war, and was biting my nails and worrying about whether
civilization was going to survive, frankly. I remember talking to Pierre when the Germans got to Stalingrad, and I was
wondering when was it all going to collapse? So we were very conscious of it. Weíd had this insulated life, but we were
conscious through the influences at home. And there were kids going off, volunteering, a lot of them were, and those were
kids who were a lot older than I was. Remember, I was two years younger than the rest of the class.
Were there echoes of sort of the political debate?
Oh, the other thing I did was I tried to get into various military programs, tried to get into ROTC, I
tried to sign-up to be an Air Force Navigator and they all said no, ďYou have glasses.Ē And I figured the possibility if
things came to war was to work hard and get into a research lab. I was not eager to go fight in the trenches, we all thought
of this war as being like World War I where the worst thing that could happen to you was being in the trenches. Actually in
this war the worst thing that could happen to you was being a bomber navigator, it turns out. So I was very lucky I wore
glasses. I volunteered with no success.
And the second part of my question was about the developments of physics and whether echoes of those reached
Then at the end of my second year, or maybe even after the first semester, they formed this engineering
physics program that was aimed at preparing kids for getting into a radar program, and some others of us understood very well
that the thing to do was to stay in physics because some of us had physicists father who knew about Los Alamos and other
things, and some of us had other sorts of information, like Ted Hall, who ended up being a spy at Los Alamos. I knew him
vaguely, but he was not in our group of physicists after the first year, but not one of the really high ranking kids. And
Henry Silsbee knew about that. He stayed in physics. But I didnít. My physicists friends back home in Urbana kept
absolutely mum and didnít advise me to stay in physics and work in nuclear physics, and so fortunately I didnít. I joined
the engineering physics program which was aimed at radar. And we also, after the first year, were expected to stay on and
accelerate our program. So I took summer school and finished in three years plus summer school and took a lot of engineering
courses. Some of those courses were very good; some of them were terrible. I also took physics courses, some of which were
good, some were terrible. It depended on the physics.
Let me try this another way. One of the things that youíve emphasized is that there was this real
revolution in the way physicists looked at the world in terms of suddenly being able to understand a whole range of phenomena
after the discovery of quantum mechanics that you just couldnít previously.
Nobody was telling us about that. We were aware of strictly basic classical physics, no quantum mechanics
in the first year. In Physics G we did a little bit of kinetic theories and quantum mechanics and so on. And in radar or in
the engineering programs, we were taught how electron tubes work, which of course is basically classical physics. We were
taught how amplifiers work, a lot of really bad classical radiation theory and electromagnetic waves, about wave guide
theory, of course, because that was very important. And not a word about quantum mechanics.
Was there anyone on the faculty that was sort of in the thick of things?
Oh yes, everyone was. I mean the faculty. Van Vleck taught us classical mechanics, but he taught us
classical mechanics in terms of the standard classical models, you know, Eulerís equations and all that kind of stuff.
Bainbridge had just gotten through inventing the mass spectrometer. Furry of course was busy doing the theory of diffusion
for isotope separation, and he taught us a lot about that after the war, but in wartime he didnít go into that. I got some
hints just in the problems. I derive from my book Maxwellís distribution, which I was thrilled when I could derive Maxwellís
distribution to really understand how a gas worked. That was a big thrill. But I didnít realize the whole thing had already
been done. There was no awareness in undergraduate school.
I learned about real physics in this odd way at the Naval Research Lab. There was this old drunk who had
had a Ph.D. in physics, he was fairly bright, but he was, you know, if loose lips sank ships, he must have sunk the whole
fleet because he couldnít keep his mouth shut about anything. I never expected that spies were that efficient. All they
needed to do was go to a bar and listen to him and they would know everything in the research lab, everything that the
research lab was doing. But he had a copy of Margenau and Murphy and Alan Murphy and I would read it, and that had quantum
mechanics in it. That was a thrill. We didnít have a lot of spare time we worked 9 hours a day 6 days a week, but there
were moments between testing antennas and things like that where I had time to read this book, and that was where I learned
about modern physics. He kept borrowing money, and finally he said, ďI owe so much money, you can keep the book.Ē I still
Are there other highlights attributed with the research lab that contributed to you headed back to Harvard
for graduate school?
Not really. Well, it was fun, but by now I was growing up and I had discovered girls and drinking and
having fun and wondering around Washington museums, all sort of things. For dinner every Sunday we went out on to a great
seafood restaurant on 7th Street SW downtown. It was very busy, but a good time.
Did you have any close family members at that point who were involved in war in other ways?
No. Well, my sister was a WAVE [feminine branch of the Navy]. She flew blimps in various peripheral
places around the coasts of the US. She never went overseas, but I think she was as far as Hawaii. But they were doing
weather assessment in blimps. She was a lieutenant in the Weather Service.
Actually while weíre on the topic, because we somehow skipped it, could you tell us a little bit about your
Well she is older. Sheís still around. And she became a biochemist, a Ph.D. in biochemistry. She and my
mother fought terribly because my mother was sexist, as everyone was in those days, and thought that boys should be
scientists and girls should primp and dress prettily. That wasnít my sisterís style. She was very much [???] When we had a
carpentry project, she was very likely to grab the hammer from me and say, ďHere, let me do it,Ē when I was making a mess of
it. Well we had a group of cousins who we were very close to and did a lot of projects at this point. She played football
with us and was very much a tomboy.
And where did she go to college?
She went to Illinois, joined my motherís sorority. So my mother, my wife, and my sister all belonged to
the same sorority under different circumstances. But my sister fought like a, bucked like a steer, but equally was a lady,
and was always interested in the intellectual things and in doing male jobs including being in the WAV. But she did get
married in graduate school. She went to Wisconsin, which was the premier biochemistry department in the world at that time,
and had a very good professor and did a very good Ph.D., but unfortunately the twins arrived the same month that she got her
Ph.D. and she didnít go back to biochemistry really ever. She tried teaching at Haverford for a while later on. Her husband
was a biochemist who became fairly high up in the Smith, Klein, & French pharmaceutical Firm. It was Smith-Klein at that
time. He shepherded several of the better known drugs through the regulatory process. It was highly regarded, but
eventually he had to basically testify against some of his superiors in a scandal they had. I donít think he was punished
for that. He didnít volunteer, he was just testifying. My sister then retrained herself as a librarian and information
assistant, basically information side of it and had a fairly distinguished career after raising the twins and another son and
daughter, she had a fairly distinguished career as a library doctor, rescuing libraries that were being mismanaged. She
rescued the library of the Hagley Foundation; the Dupont Companyís History of Science division. She rescued the library of
the University of Pennsylvania Medical School. She rescued the library of the SUNY, Binghamton at various times. And she
and her husband both have an interest in the history of technology and have published papers in that field, and a book.
Given that she was ahead of you and also doing science, did you have much of a dialog with her as you were
I was a little guy who hung around. I was five years younger. Of course I was a younger sibling and she
and her friends would brush me off when they could and occasionally would be very nice. We were always close. We never
really fought more than siblings do. We were part of a group of four very close cousins. I had two cousins in the
Crawfordsville and there were the two of us, and we always vacationed together for Christmas, Thanksgiving, Fourth of July,
and so on, and we did everything together. My cousin Dick became Lieutenant Governor of Indiana. I was close to my cousin
Jim, who also was the same age and was very close. And the four of us got along just fine. We did a lot of things together.
So letís get back to the war essentially, and go back to the Naval Research Lab. What made you decide to go
back to Harvard?
I went back to Harvard because I felt Iíd been cheated out of an undergraduate education in physics. And I
met Van Vleck on a couple of occasions during the war. After we got through designing countermeasures, I guess I covered
that in the other interview when I was talking about the war. But after we got through the main effort, we got interested in
what was going to happen after the war in propagation, and well, the programs, the research lab actually did do after the war
in rockets and space. We got interested in propagation and propagation of microwaves and radio waves in general. So I went
to some conferences on propagation. I saw two of my Harvard professors, Van Vleck and Furry again, and some of the people I
was later to know at Cambridge took part in this meeting. I was very, very impressed by these guys and various phenomena of
propagation of microwaves and wave guiding effects where weíd get enormously long propagation over water and things like
that. So I looked at it and I thought, ďThis kind of thing I can develop happened at Harvard.Ē Really interesting stuff, and
I wanted to go back. I couldnít, I didnít — You can see I wasnít very imaginative. I went back, slept on Tom Kuhnís couch,
and Van Vleck cane back, and he said, ďFine.Ē So I came back. I was discharged in October and two weeks later went off for
Schwinger arrived in, letís see, I started in October. Schwinger arrived I guess in February, the second semester. I
was taking quantum mechanics with Furry and statistical mechanics from Furry, and simultaneously Schwinger was giving this
marathon course starting in February for three semesters, a fascinating course because essentially he had changed everything
that he had learned in his life for three semesters of hour and a half lectures, and you just had to be prepared to miss
lunch because he started normally at noon to 12:15 when he walked in to give the lecture, prepared for what he was going to
say. He never had notes to lecture. Heíd be writing with both hands for an hour and fifteen minutes, and then we would rush
and maybe were late for lunch. And all of us, everyone took that. There was a lot of physics, variational techniques for
solving [???] and variational techniques for solving a deuteron. So we were already in good physics, what are nuclear
moments about, how do you do nuclear moments? What about symmetry? Angular momentum and how you deal with it in nuclear
physics. A little bit of fission. The second half you have Bethe. We used his article in Modern Physics in our textbook.
Furry taught out of Pauliís Handbuch article, and the gang was trying to translate that. I must say I think I did a
pretty good job with my chapter, but most of the chapters were absolutely abysmal because most of the kids didnít even
understand physics, so it wasnít much help. So we were learned German. The next year I took Group Theory from Van Vleck,
and I still had an annotated copy of Wigner in German. Then we had some terrible courses. There was a course in elasticity
which was supposed to be taught by Hilderbrandt but he was busy worrying about the elastic properties of lung casings and
never showed up at all and von Mises gave it. He was in the Applied Physics department. He was in fluid dynamics and he
taught it very badly.
The courses in general were good, and we worked over the summer. In the summer, Goudsmit came out and taught a course
in ďFun with Variational Method.Ē It was supposed to be classical mechanics, but he did it on the variational method, and he
had these wonderful examples in which with a Dutch accent he would talk about the bug going on a wheel, and they would be
crawling around the edge of a wheel and the wheel would be going in such and such a way. He was a marvelous teacher. The
only solid state physics I ever had wasÖ I had two very good approaches to solid-state physics, neither was solid-state
physics. Gorter came and told us all about [???]. He talked about how they worked during the war. And the other was
Brillouin who came and gave this beautifully precise explanation of periodic structures using his book. These were all kind
of extra summer courses. Another thing was Furry didnít do statistical mechanics, Furry did kinetic theory. And that was
what Furry liked to teach.
Who were some of your fellow students, names you know of?
They were very high quality people, a lot of them working with Schwinger. Bob Karplus, Walter Kohn,
Branscomb. Rolf Landauer was younger. He was a close friend of Wendell Griffith from Urbana. There was a group of younger
guys who I interacted with some. Bloembergen was really a post-doc, but was in some of the classes. Tom Kuhn of course.
Ken Case and I took or analysis together. It was an awful course by a mathematician called D.V. Widder in which he undertook
to do all of the complex analysis without ever doing a single contour analysis. He did it all by Mittag-Leffler Series and
Taylor Series and all of the possible kinds of series and continued products. Ken and Tom and I worked very hard. We would
always look at the homework papers, but we hadnít all gotten 5 pluses. It was very competitive.
Speaking of Tom Kuhn, I mean at this point did he already have some inklings to the kind of work heís done
in the history stuff?
No, he was doing a very good thesis with van Vleck. He was much more mature, a much more mature physicist.
I knew very little for instance, I was very surprised when I looked up from the roof at the Naval Research Lab and saw the
first jet plane some time in 1944 when it was still secret. That was one of the first tips in the war in what was going on
in the Army Air Force station next door. I said, ďOh my god, what was that?Ē It could have been something bad for all we
So to set the stage for your choices, the thesis problem and so on, a graduate student entering today faces
in the physics department fairly well-defined specialties, groups. What was your sense of physics as you began to come to
grips with the research project?
Well, there certainly was no group structure. I mean everybody was either a theoretical physicist or
experimental physicist. I took what I had to take in physics and I enjoyed it. There was a wonderful course by Oldenberg in
which he made it a point of rescuing historic experiments from the dustbin and Bainbridgeís first mass spectrometer. He had
an oil drop experiment, I donít think it was the original one, but it was the first generation after that experiment.
One of my closest friends was Al Sachs. He was working for Purcell. He became a particle physicist and did NMR. My
roommate was Rod Cool, who became a particle physicist. He was working on Spark chambers, but he was taking the same
courses, doing the same routine. And a lot of my friends were working in chemical physics where many of them worked with Jen
Wilsonís father, E.B. Wilson in microwave spectroscopy. So we didnít differentiate. All of us who could managed Schwingerís
I made my choice because I kind of liked that in van Vleck. Schwinger had far too many people outside his door. He had
about ten minutes for each of his students every week or so, not that I saw Van that much, but if I wanted him, he would have
been there. He was available when he wasnít on sabbatical or in Europe somewhere, but when he was there he was there. So I
more or less chose on the basis that I wanted to work with the guy who was around and was available.
The other thing that I had become fascinated by was the Gorter course and by learning about my friends who were doing
microwave. So I guess when I went and saw Van, I said, ďWell, have you heard about the good things with microwave
spectroscopy? Maybe Iíd like to do something with that.Ē
Your thesis work, you were starting to tell us about the problem that happened close to you, spectral line
problem. Could you tell us a bit more about that, what the state of your knowledge was and how the problem was disposed?
Well the spectral line problem, he gave me essentially all of the literature that there was on spectral
line breadths was where anyone had made any effort to do a quantitative job which consisted of basically there was a long
paper by Weisskopf who was trying to do it semi-classically using quantum physics and WKB. There was the old Debye-Lorentz
collision literature which was kinetic theory, molecules banging against each other. And then there was a paper by an
obscure Swede named Lindholm who worked in the forest products laboratory. But he had actually done the most advanced thing
ever done and was mind broadening because he actually thought about how the forces that influence the line and how the
molecules approached each other and modulated the spectrum of the light that you were getting from it. So kind of in
principal the starting point was Lindholm. And then there was a paper by Margenau who had done what he called the
statistical theory and that was very puzzling. He got roughly right answers, but he had the molecules sitting absolutely
still, and that was a hint from which a lot of things followed later on. But I didnít pay much attention. I didnít worry
too much about it in the thesis. But you know there were literally thousands of new data in this field.
People had done sodium atoms and the sodium lines, and people had done stuff comparing Doppler broadening
with pressure broadening. And then there was a little data on a couple of vibrational bands of simple molecules. And now
all of a sudden you could do say a 100 lines in the ammonium inversion spectrum and each one had a different breadth and then
they had systematic variations of the breadths, and there were literally thousands of lines in the water spectrum, which was
much more complicated because asymmetric.
It was the fact that a certain frequency range had become available that had caused these variations?
Well, it really was just microwave techniques. In the past we had always done the incoherent spectrum
because light sources, thermal light sources had only incandescent bulbs, not lasers All of the sudden we had coherent
sources and we could study and a line by taking the frequency of your transmitter and running through the line, or if it was
a magnetic resonance line, you would keep the transmitter fixed and move the magnetic field. And Bloembergen was doing a
similar thing with the magnetic resonance spectrum, thinking really physically about what caused the shape of a line. I was
close to the gas spectrum, all of the gases that we were working with over in Bright Wilsonís lab, and Charlie Townes was
busy doing it all here at Bell Labs and at Columbia. Bleaney was doing it all at Oxford, it was all taking place at the same
time. And so there was lots and lots of data, and Van was smart enough to realize that it was going to happen and it was
time we had a theory of line broadening. He could take care of the frequencies involved with lines, and that was the theory
of the 1930s with a lot of bells and whistles. But all he knew of to worry about actual details of the line shape was this
strange thesis of Lindholm. He handed that to me, and told me a few facts about the code name to look up some facts about
molecular interactions. And I was busy.
I was very much involved at that time with a group, Tom Lehrer, Dave Robinson and so on, having a very good time
playing bridge and doing double crostics and singing, generally not really carousing but doing all kinds of extracurricular
things. And in the summer of 1947 I went home and met a girl who I had actually been the closest friend of the cello player
in our quartet that I had in high school, but for some peculiar reason, neither of us can figure out how we never met. And a
month or two after we met, maybe six weeks after we met we were married. She had come to New York with a recommendation and
was in training to be a junior executive in the Coca Cola Company, and they were determined that they were going to give her
the entire South American concession. She could have been a millionaire. Instead she moved to Boston and set to work for
35 cents an hour, the typical Harvard wage, in the bursarís office and we got married and lived in this miserable hovel near
the square. But then she went home to Urbana, lived with my parents for a semester to make enough money so that we could
afford to have the baby, and concealed her pregnancy successfully from the English Department because they still had anti-
nepotism rules at that time. Anyhow, so I set to work on my thesis, and at the same time Van Vleck called me in and said,
ďAre you doing anything?Ē and I said, ďWell, yes sir I have been,Ē and he said, ďWrite something up for me.Ē So I quickly
wrote up a few sheets of paper, and on the cover I wrote, ďDear Van, you old bat,Ē and tore it off. I wrote some things
about molecular interactions, and that was enough writing to let me go on with the thesis. But then in that semester I had
the basic ideas of the thesis and by the time Joyce came back and had the baby, it was Ď48 and we typed it all out in the
fall of Ď48 and then went off to Bell in Ď49.
Let me sort of ask the more precise sort of physics questions. So this Swedish work that you alluded to, so
when you came to the problem, what was understood about line broadening? What were the sort of technical and conceptual
obstacles that you had to deal with?
I wouldnít say it was understood. Lindholm had this idea that when two molecules get close together, they
modulate the frequency of the lines that one of them is admitting because that frequency modulation starts out with a new
phase after the correlation. So that makes the phase change by a certain amount. You can call that a collision. So he had
this idea that phase modulation is the crucial thing. What I had to do was two things. One was to generalize this to
degenerate levels. There were rotational levels of course, but all rotational levels in a gas. There is very little
rotational degeneracy, so youíre going from a J equals something level to a J prime equals plus or minus one level where you
have all of those rotational degeneracies. So what you have is a scattering matrix. So my basic idea was, instead of this
change in phase, there is a scattering matrix. Thatís the unitary transformation of the state of the molecule that it
undergoes after the course of the collision. Then I had to figure out how that unitary transformation affected the line.
The first place I would calculate that unitary transformation in terms of the integral interaction of the collision . And
Lindholm had only a primitive way of doing that. I mean he said that to really do it with phase alone, we had a pretty good
approximation for two molecules which are passing each other on approximate paths, and that I borrowed from Schwingerís
course because he taught me about how to use the unitary time development matrix of an equation, and that what you really
wanted was T, the S matrix, which is the change in the T matrix in the course of the collision.
Then the question was how does that affect the line graph? So I figured that out and worked out an expression for it,
and then I figured out some very good approximations that I could use to give the complicated sum of these matrix elements
over the entire range of impact parameters. I figured out some good approximations for that, so then I could calculate, I
knew the forces between an ammonium molecule say and a argon atom, which are just given by the van der Waalsí attraction
between the polarization formed on the atom and the dipole on the ammonium. Then I got the cross section. And I did the
ammonium spectrum, and I looked at these results and it agreed, actually, in considerable detail with these results. The
only thing is I said, ďWell, these two lines he got wrong.Ē And that was amusing because Bleaney of course was the senior
professor, the Clarendon professor the professor of experimental physics at Oxford, and he came and visited us at Bell Labs a
few months after I had gotten to Bell Labs with Miss Plumpton, who was soon to become Mrs. Bleaney, and I explained this to
him and I said, ďWell Iím sorry I got these two lines wrong,Ē and he laughed at me, and he went back and measured them and
[???] wrong. But he never told me. He did tell me much, much later when I got to know him fairly well that I had got it
right. I was this green, green kid and I couldnít be telling the great Bleaney that I got his experiment was wrong. I had
grown up with this bunch of senior professors and I was used to telling them things. I should have been afraid, but I wasnít
The totality of the data that you explained was that presumably there were systematics the gases and
Yes, I did that ammonium spectrum. I did, I think it was a rare gas. For infrared Iíd get a couple of
the classic vibrational lines that had been done in an old- fashioned spectroscopy. And then I said, ďWell, Iíve done it in
principle. Iíll do a couple of others.Ē Some estimates on a couple of others. I had those things done in principle, and
there was enough detail on the ammonium, so that was complete.
Looking through your thesis papers written out front, there is a stochastic idea that you used. Was it wide
spread at that time?
No, I was inventing a lot of this stuff. Number one, proofs without knowing it. I was using fluctuation
dissipation theory without knowing it. Well, there wasnít a fluctuation dissipation theorem. There were only the Einstein
coefficients, but actually the Einstein coefficients really do contain the entire fluctuation dissipation theorem. If you
think about it, Einstein was very bright. Back in 1905 he figured out there was a fluctuation dissipation theorem, and he
found the ratio of spontaneous to induced emission. He showed that the dissipation, which he deduced conceptually, can be
calculated from the spontaneous emission with these fluctuations. So I was calculating spontaneous emission. Of course you
canít measure that in the microwave region. Just take B over A and that will be part of the induced absorption. So I was
And the other thing was I really was doing a statistical stochastic sum over all possible collisions averaging over the
impact parameters for the velocities and so on. I was doing it in a rather crude way. And those spontaneous emissions,
well, spontaneous emission was actually, the spontaneous fluctuations of the dipole when we looked at the whole sample.
Actually that was the case. So I realized that the point in principle, that the spectrum is the result of the spontaneous
fluctuation, the dipole moment of the whole sample. I was kind of fascinated by that. I remember Joyce asking me, ďWell
youíre doing this very niggly little problem that seems very, very specialized. What general meaning does it have?Ē and I
said, ďWell, I can really understand whatís going on in a real sample of gas.Ē That stands for a real substance and I
thought that was important, because not many people had ever done that that I knew of.
Schwinger was in fact the very influence of, along with Paul Martin, in the development of the sort of modern
apparatus, the correlation function. Was this work already in progress that you interacted with that string of development
Not really, well, Iíd heard it in his course essentially. I donít think I actually talked with him. Well,
there was Schwinger and Karplus. They did a theory of line broadening in magnetic resonance, and it was a kind of general
theory of line broadening. I guess I must have talked with Bob Karplus. Mark Karplus was the younger brother who still is a
successful chemist. Bob went off and got interested in high school education. He was probably brighter, Bob was, but he
never amounted to very much in terms of research, which is of course where the good project comes from a high school
education. So he and Schwinger had done some work on these lines. They had kind of a generalized formula for line breadths
which was related to this. But of course, the S matrix stuff I just borrowed straight from Schwingerís course. And in order
to do this problem, you had to take an S cross S, an S that is a direct product of the S matrixes and one for the initial
state and one for the final state. So it was a little trickier than that at this point.
So what happened in solution to this problem from the time that you ended up at Bell, how did that go?
(There were too many papers by chemical theorists about my methods.) Well, I went to Bell twice. The first
time was during this gestation period. Joyce was in Urbana teaching elementary English. And I went on a tour of various
laboratories looking for jobs, and recruiters had been around jobs in these various places. I had put down in some sort of
questionnaire that I wanted an industrial job since I was married and post-docs didnít go to married students. Itís hard to
realize that I was, but of course I was.
Could you elaborate on that for me?
I donít think in those days you got married and went off to a post-doc. You postponed what plans you had
until youíd finished your education. So post-docs were out of the question. I could go and become an assistant professor,
and assistant professor jobs were not out of the question, or I could take an industrial job and I couldnít do a post-doc.
Was this a question of salary or was it more than that?
I think there would have been a prejudice against us. I think some people did have problems. The standard
thing was, you finished your Ph.D., went off to Europe for a year in some place or another, and then you came back and got
married. But I didnít finish half of my Ph.D. so I didnít have a choice of a professorship and an industrial job, and my
mother thought that since she had lived on an academic salary all of her life, that an industrial job could pay better and I
didnít disagree because I admired Bell enormously. But I went there and I didnít have much to say. I just had this little
bit of stuff that I had done. I was just thinking, I remembered actually on the train on the way back, three or four basic
ideas of my thesis and really not very much more, and how to do this cross section. Some part of that came to me on the
train on the way back, but I had just had to discard the problem and see how the interactions affected the line. I couldnít
say I had solved the problem. And they were very polite to me and sat and failed to hear John Bardeen say anything because
he never said anything, even in interviews. I talked to two or three other people, Charlie Kittel, but I didnít impress
And later on I went on a recruiting trip to GE, Westinghouse and Brookhaven. And by this time I had my thesis and was
writing it up, and both Westinghouse and GE were quite interested in my career. John Holloman was in charge of hiring at GE.
He couldnít persuade his management, Harvey Brooks, that I was worth hiring, so Harvey Brooks turned me down there. Sammy
Goudsmit turned me down at Brookhaven for a reason that, when I was asked what I wanted to do know, I said, ďWell I finished
my thesis. I want to do something else.Ē And he said, ďThis man canít have really done a very intricate thesis if he
finished it.Ē Well the fact was I had creamed the thesis. There was no more interesting stuff to do. I had done all of the
interesting stuff, and I was sure I had done all of the interesting stuff and I needed new problems, new worlds to conquer,
but Sam Goudsmit actually refused to believe that, even though he rather liked me and I had been a recruit to when he spent
an evening with a case of beer of talking about the Alsos exhibition when he was at Harvard. He turned me down.
Westinghouse wanted me because Ted Holstein was there and he had been interested in what weíd done. But Ted couldnít
persuade Westinghouse to let me work for him. They insisted that I should go and work in transistors, and they had a big
room and they had eight chairs in which I would have been the first to be occupied, and there would have been a tray of
transistors and I was given them, and I was supposed to figure out how these damned things work. This is the level at which
they were. So I had that offer, and then I had an offer from Pullman State College in Washington, which wasnít the
University of Washington; it wasnít a real institution and had no graduate program.
Nonetheless, I chose to go to Washington and we borrowed money from my parents and bought a car and we were going to
drive across the Rockies in the winter and get to Pullman, Washington when Van finally called me and said, ďWhat do you want
to do?Ē and I said, ďI want to go to Bell. Itís got Bardeen and itís got Kittel, it has everybody I ever heard of. They
actually invented this thing that Westinghouse wants me to work on, which I knew about, and they have Charlie Townes, and
theyíre working in my field. I want to go to Bell.Ē And then Van went to Bell, on the Phoebe Snow (the Lackawanna
railroadís crack train). It is not an apocryphal story. He actually did ride in the cab with of the Phoebe Snow because
railroads loved him so much because he kept their schedules straight at that time as a hobby. And he rode in the cab, got
off at Summit, went and talked to Bill Shockley and he said Bill Shockley would hire me. And Shockley came up to whatever it
was in Boston and interviewed me, and he said would I work as a post-doc for him, they didnít have any room for regular jobs
and I said no, and he said, ďWell weíll hire you anyhow.Ē And of course I didnít know that all of the contracts at Bell Labs
were annual so that he was quietly in his head reserving the right to fire me after a year as a post-doc. So I went to Bell.
What in your thesis did Van like?
I donít know, except that, first he insisted that I rewrite it; he said it was all Germanic English. Then
he insisted that I put in a chapter in which I explained how you could get my result semi-classically, and I thought I had
figured that out, but in fact that chapter is entirely wrong. You canít explain these results semi-classically. But I put
it in anyhow. But then he brought in Schwinger and Weisskopf, and I should have known when he did, that my thesis committee
was the indication that he was proud of it, because he wouldnít have exposed himself to Schwinger and WeisskopfÖ And I think
then when he decided on the thesis committee he decided heíd better find out where I was going to work.
How did your thesis defense go?
They just didnít know beans about what I was doing. [laughs]. It was very easy.
So much for that. So that brings us to that. We turn to arriving at Bell Labs. So there are a number of
questions here. Can you just give us an impression of what is was like when you first arrived at Bell? Who were the people
who were there? Who were the main players, and who inspired you?
Well, I was thinking about that last night. Thatís when I said well we should think about social groups.
The first place when I arrived, we were two people over whatís called nose count. They counted the noses, but didnít divide
by anything. It was the number of desks you were supposed to have, jobs you were supposed to have. In that same month they
brought in Bernd Maatthias, John Galt, and Gregory Wannier, and myself. Gregory and I, I believe, were the two who were over
nose count. So we were put temporarily in a room together which had previously been a conference room. What I didnít know
was that he was busy getting rid of John Richardson, who was a very nice fellow, who for some reason failed totally to resent
my presence even though I was obviously his replacement. And then I got an office to myself.
Things went very fast. For one thing, a lot of us were new, so we got to know each other fairly quickly. There was a
little orientation course we had to take in which we were shown the telephone switches going click, click, click. Of course
they were all relays at that time, and they explained how all of this happened, but it wasnít too important. (I guess I
didnít mention taking the radar course yet at the Naval research lab).
But very soon, I donít remember exactly how it happened, I got into a little group of people who went to lunch
together, and the kind of a leader was Alan Holden who was a non-Ph.D. chemist who had been at the labs ever since 1925 or
1926 in various jobs, but had only joined the research department relatively recently. He was the man who did all of the
preparatory chemistry for Charlie Townesís molecular spectroscopy. He also did a lot of preparatory chemistry for later work
in magnetic resonance. But there was this little group, and then Alan insisted on actually having a sit-down lunch in the
service dining room. So we would go every day and have a sit-down lunch. Somehow we got Gregory in on it. Gregory and
Betty Wood and Alan and I were the core of this group, but a number of people joined us very often. Stan Morgan was a
department head. Charlie Kittel often came with us. Charlie was close friends with Alan Holden because he was building a
house in Harding Township near where Alan lived. Bernd Maatthias often worked with Betty Wood who was a crystallographer and
he needed her skills as a crystallographer because he was not strong theoretically, to say the least.
And we also needed her to look at his crystals that he saved, what their quality was and so on. I remember
people joining us, and when Hal Lewis came, which was a couple of years later, thereís a complicated history involving
refusing to sign the oath in California. He was going to the Institute and going to Bell Labs where we didnít care if he
signed the oath so long as he kept his clearance, which he did. So he joined Bell Labs, and he was very much a member of
this group. So this was a group and again this was not the follow-your-nose, work hard, do-good-things-for-the-company, and
do experimental things. It was not that many people. At lunch we talked about politics, we talked about art and music, and
whatever the hell we pleased and sometimes about science and when we talked about science we were generalizing questions
about how, for instance, was a quantum solid? Gregory was interested in wiggly bands, why didnít diamonds conduct
electricity. So it was kind of a broader group, and also very, very politically active. From that table came the only three
people who refused to sign the oath, which was a ďsecurityĒ questionnaire sent to all of the people at Bell Labs, Gregory and
Alan and me. So that was part of a socialization and it was very useful for me because I didnít know beans about either slid
state physics or solid state chemistry or crystallography. Alan and Betty knew all about that. So that was very helpful.
Charlie appointed himself more or less my mentor once I disengaged from Bill Shockley. And Bernd of course was always a very
close friend and often a kind of love/hate relationship, but there was much more love than hate. But he had that
relationship with everyone. Bob Shulman eventually joined this group later on. He was more involved in the Chemistry
Department at that time.
At the same time I got to know fairly well Bardeen and Brattain particularly. We were bridge players and we formed a
team of four. That was with John Hornbeck and Walter Brattain. I think we even came in second in the labís bridge
tournament. And well there was really no problem with socializing. I mean we worked very well, had the journal club,
political science, and it was very informal. There was also plenty of pressure to pay attention to the experiments that were
going on, and it was welcome pressure. I mean I was very interested in the kinds of things that were going on. I was very
interested in Berndís work on ferroelectrics; I wasnít that interested in Bill Shockleyís ideas on ferroelectrics, but I was
interested in what he was doing. I was interested in the magnetic resonance work that was just being setup at that time.
Alan was providing the crystals and Charlie was thinking about it and Bill Yager was doing the experiment to begin with. So
there was no problem with being interested in the experiments, but very quickly somehow I got to be quite good at talking to
experimentalists and being interested in what they were doing. So I fit in fairly well. Shockley, well, for a year I worked
hard on Shockleyís ideas on ferroelectrics, and honestly did think about ferroelectrics and in particular with Gregory we
thought hard about phase transitions. Gregory was obsessed with Onsagerís work in the Ising model. He was in some ways a
little [???]. He was not the best known of the theorists who were there, but he was the most conceptual of the theorists who
were there. He was really interested in how exactly do you define position in the Brillouin Zone or in a band rather than
the position operator of a real electron? How do you define the position of what we would now call a quasi-particle rather
than a real particle? And thatís the Wannier function. He was really aware of all of the Wannier function questions that
later on would become things that add up. I should have said Walter and Quin were very much in this lunch group.
Would come in, in the summers?
They were there summers, most of the years, certainly after I got back from Japan, [???] and Quin were part
of this gang of people. It was interesting that someone in the center was Alan Holden who was really almost an unknown. He
was co-author in a number of famous papers, but not well known, co-author on the early work on magnetic resonance at Bell
So I had a number of follow up questions with that. Actually I noticed that you wrote a number of papers
with Richardson, who you were there to replace in fact. Can you tell us a bit of the particulars, it is a very nice paper on
general theory of phase transitions, discussion of the theory of phase transitions? So the two of you must have discussed
Well, Gregory really was the instigator of that. He and Richardson went to a conference on phase
transitions that I didnít go to, and when they came back and they discussed it. Well, I guess at that conference Tisza had
presented his general theory of phase transition, that the phase includes the Landau order parameter. Landau never admitted
that the Tisza theory was the same as Ginzburg Landau, but it was the same and the principle was an analytic expansion of the
free energy as a function involving macroscopic parameters, and you predicted phase transitions thatís where the free energy
became unstable to go over to another phase. It was very similar to the Ginzburg-Landau. We didnít know of Ginzburg-Landau
at that time because that was the period of blackouts in communication. But we had Tisza and Ginzburg-Landau. Gregory and
John had discussed this and Gregory said, but Onsager has this phase transition that doesnít satisfy this transition theory
and they got to talking to me, and I said, of course it isnít, and we resumed discussion among the three of us after we
decided Onsager is a very good example of the fact that analytic theory, just doesnít work. And I think this is maybe the
first published reference anywhere that says, because of Onsager, the standard theory doesnít work. Now Gregory knew that,
so it actually wasnít because of Onsager, it was because of Kramers-Wannier, because Gregory had deduced from general
arguments that in fact they have a lot of symmetric logarithmic [???] gave a symmetric logarithm that [???]. That was
predated Onsager and that was Kramers-Wannier. And so we looked at it and we decided, well, the spectralization wasnít
going to be analytic. Really nothing was going to be analytic. The critical point was not an analytic point, and we
actually pounded on the table and said, contrary to the thesis statement, the critical point isnít analytic. And I think
this was the first published version of that. But itís just a comment.
And I noticed that.
But John was still there at the time, and it was a common point with Gregory.
Now suddenly we see the evolution of your interests, ferroelectrics you mentioned, but also suddenly we see a
new interest in magnetism with the rise of your interest in super exchange. How did you get interested in super exchange, in
exchange and anti-ferromagnetism? What were the motivating experiments out then?
That was Charlie Kittel, straightforward. Well, Gregory and I were still in the same office. He walked in
the office door one day and said, ďThere is this new thing called anti-ferromagnetism. Are you interested in it?Ē And
Gregory was interested in it because he thought, ďWell, letís do an Ising model with anti-ferromagnetic interaction,Ē and he
realized that for the square lattice itís the same model because itís also the Bragg-Williams problem. He tried the
triangular. It looked much more interesting, and he played with that for a long time. And actually I think it was Charlie
who said there is this funny paper by Kramers a long time ago that says, interactions happen between magnetic atoms quite far
apart, and I realized through Charlie that if MNO was a ferromagnetic, if you drew atomic radii for MNO, you have great big
oxygen. The manganese were quite far apart. So I set to work to think about Kramersí paper and how did it happen, what was
responsible for interactions between atoms that were really quite far apart, exchange interactions. And I wrote a paper,
exchange number one. There is this Neel paper about anti-ferromagnetism, and then we discovered Van Vleckís old paper. I
said, ďBut of course if exchange interactions are the way that Kramersí theory suggests that they are, then the interaction
between next nearest are comparable to the interaction between nearest atoms, and if we set these up in a certain way,
strange ratios of thetas to TCs will fit very nicely. This was stimulated by Charlie. Charlie saw to it that Shull was
invited to give a colloquium and we also listened to him and he talked to me in detail. This was the second point: that
there was a certain amount of friction between me and Shockley because the friction came between Charlie and Shockley.
Charlie was usurping his post-doc. And here I was doing these things in anti-ferromagnetism instead of doing what I should
have been doing which was working on Shockleyís ideas on ferroelectrics. So that caused some friction. Well, I talked about
all of those political things for the other interview.
But then that was Charlieís stimulation, and the fact that I realized very quickly that this little quirk of the Neel
theory as explained beautifully by Van Vleck back in the Ď30s that you can get any ratio of theta to TC if you like even
though both were perfectly good measurements of the exchange interaction. We had a way of quantifying the exchange
interaction just by comparing theta to the TC.
Theta being the Weiss temperature?
Weiss temperature. That was kind of my first Bell denominated success because I was invited to give a
paper at the Oak Ridge meeting and once I had an invited paper, I was immune to whatever Shockley thought about me. I was
safe. Then Morgan would protect me after that.
This was spring 1950?
Spring 1951 that I was writing this paper. Van Vleck came and listened carefully, and then he went off to
one of his ubiquitous meetings in Europe, and it may have even been the Solvay Conference. His talk featured entirely all of
the work Iíd done on anti-ferromagnetism and the fact of that got back to management. And after receiving a minute raise,
which I was very proud of, in the first year, all of the sudden I got a respectable raise the second year and then we could
afford to buy the house that we then bought. Before that we were scraping along just barely because we had borrowed to pay
the deposit and rent and we had borrowed from my parents to buy a car. I guess for quite a period what we had was a card
table and four chairs, and then I remember entertaining Shockley, inviting Brattain and sitting at the card table and four
And so your second paper on anti-ferromagnetism, actually the lead up to that was the limits on the energy of
the anti-ferromagnetic ground state, and you presumably start to think about zero point fluctuations somewhere along the way
there. What led you to start thinking about the quantum fluctuations there?
I donít know. Somebody reported, Jerald Clog [?] or maybe Charlie again brought it to my attention. I
donít know. I must have read Martin Kleinís paper about ferromagnetics, and we were interested, various of us, in spin waves
and ferromagnetics and spin wave theory in general. I think it was a question of Charlie, ďWhat about spin waves and
interferromagnets?Ē And he I guess had developed a theory of the frequency for ferromagnetic resonance, and I got interested
in the theory and the frequency of anti-ferromagnetic resonance and I realized that that was a special case of the general
question of ferromagnetic spin waves, found this paper of Martin Kleinís actually referred to a Kronig paper about classical
theory of spin waves, the fact that all spin waves are a purely classical phenomenon to begin with. The spin has a classical
spin. We calculated the classical equation of motion just using M dot equals M cross H, and put the exchange field in there
and then classically imparted the function. Martin Klein had taken that proto-theory and said, ďLook, it even fits in the
case of ferromagnetism if you do the quantum mechanics right.Ē Except for a smidgeon, it makes the ferromagnetism including
the zero point fluctuations of the spin waves become the classical theory of ferromagnets the same as the quantum theory of
ferromagnets. We realized, ďAh, you have to do anti-ferromagnetism,Ē and that was the quantum theory of the anti-
ferromagnetic state. We had been worrying about the anti-ferromagnetic ground state, Gregory had, I had, Charlie had, and I
realized when I looked carefully at the nuts and bolts of Peter Weissís theory where he had tried to do classical cavity
theory on anti-ferromagnetism and he got an answer which didnít make sense. So I realized how the quantum theory didnít work
because it had a divergence in the zero point fluctuation. And that was the other paper that became important because of the
ground state. But I had been thinking, ďHow does Weissís cavity theory compare with classical?Ē
What was Weissís cavity theory?
He did a quantum theory on Bethe-Peierls. It gives you a rough approximation at Tc. But it makes
nonsense with the anti-ferromagnet. The mean field disappears at low temperatures because the fluctuations diverge, and so
when T = 0, the quantum fluctuation destroys the point of that theory.
So weíre convening again for the second time interviewing Phil Anderson now for his period at Bell Labs in
the Ď50s. Phil, last time we spoke weíd been talking about your note with Gregory Wannier and Richardson about the
realization that mean field theory wasnít good enough to explain phase transitions. Just when we finished you made some
interesting remarks about your efforts to look at non-linearities in Landau Ginzburg equations.
Well, for two summers, Jim Talman, who is now a fairly eminent relativist, I believe wrote a book together
with Wheeler and Kip Thorn, something like that anyhow,he is quite eminent in general relativity. But for light recreation
in the summers he came up to Bell Labs. I didnít know at all what he was doing.
This was Misner, Thorne, and Wheeler?
I guess it was Misner and it wasnít Talman, but Talman worked with Misner and with Thorne. Anyhow, he was
another Wheeler student and became a relativist. And the first year he worked with me on a problem in line broadening, which
was amusing in itself and was nice because, again, we really clobbered that one, and the solution we found was rediscovered
20 years later by Ulrich Frisch and he made quite a thing of it. The second summer I thought I could relax and do something
interesting. By that I had become very interested in this problem of a critical point and phase transitions. We fooled
around with several things, but particularly we used as a model what essentially, the same models that eventually Ken Wilson
used to actually solve the problem, essentially the fourth theory in classical form, soft spins. And I developed a diagram
series for it which was essentially the diagram series that various people later used. We didnít get very far with it.
Basically I identified the diagrams which diverged in low dimensionality, but I never found a way to add them up in any
sensible way, nor did Jim. But essentially we realized that they didnít diverge in five dimensions. We werenít as smart as
Pokrovsky and Padashinsky who realized that they could be converged logarithmically in four dimensions. So we didnít get
that far, but we did show that they didnít diverge in five dimensions. But we never published anything on that.
At the same time I was very interested in the reaction field, the local field and tried to find some formal way, some
way of formalizing in a better way what Onsager had done in developing his version of the local field. Again, I didnít
succeed. Thatís just a lot of stuff in notebooks, but there was an interest in this general field and realized that things
hadnít really been properly solved, but I just wasnít able to do much with it.
Thank you. Just as an aside, actually, you mentioned diagrams. What kinds of diagrams did you draw, Feynman
Well the diagram series had very legitimate classical foundations in the idea of cluster expansion.
Gregory Wannier had essentially pioneered that particular art. He at least realized that Mayerís diagrams that he used in
classical statistical mechanics were essentially equivalent to a Feynman diagrams. And Gregory, without actually formalizing
the linked cluster theorem, had long since developed a method for demonstrating by just playing games with powers on the size
of the system that the unlinked clusters dropped out. There was always a cancellation between numerator and denominator, a
cancellation of the diagrams against the Z in the denominator. That was all his business, not mine, but I was using
essentially these diagrams and realizing I wasnít going to run into trouble with the unlinked clusters.
We wanted to turn to ask you a bit about your interest in ferroelectrics. In particular, it seems that
looking at your paper on the theory of ferroelectric behavior in barium titanate that many ideas that foreshadow later
developments took place in this paper. In particular some of your early ideas about broken symmetry applying, a symmetry
breaking field are to be found in the paper and I wondered whether you could tell us a bit about that.
Well, there wasnít anything very sophisticated in any of this stuff. I guess I learned about free
energies. I had taken thermodynamics in graduate school, but unfortunately I took it from Percy Bridgman. Bridgman had the
most soporific voice of anyone I have ever heard. But he insisted on lecturing at 8:30 in the morning, and by 8:35 I was
asleep and most of the rest of the class was asleep. So I learned essentially nothing about thermodynamics. Furry had never
done statistical mechanics. Well he said, ďStatistical mechanics is easy, and so Iím going to do kinetic theory,Ē and spent
most of his time doing kinetic theory, which was very useful and it was nice to know. But I never understood what free
energies were or any of that stuff. So I learned my statistical mechanics from Conyers Herring and Gregory, and so coming at
it anew, Conyer had already seen the relevance of the free energy undergoing a singularity and breaking into a two well
potential and so on. Heíd seen how phase transitions go, so without knowing about it, we understood the Ginzburg-Landau
theory and I was playing with things like that. Otherwise I donít think there was anything that wasnít basically in the air
at the time and much of it I would have ascribed to intuitions that Conyers particularly had.
When you said you learned things off people such as Conyers Herrings, what was the mode for learning? Did
you pick it up on the fly as you were trying to do research or did you actually sit down and go through things together?
Oh it was strictly on the fly in discussions of various kinds. Or I would wander into his room and ask him
and he would say, "Well maybe this kind of point of view would be." Gregory and I talked a lot because we were rooming
together for that relatively brief time. Otherwise it was all extremely informal.
All right, letís move on. Now it was around this time that you went to Japan.
Yes, well that was a consequence of the anti-ferromagnetic spin wave theory, more or less. Well two
things, that and my NMR work.
Maybe we should touch on the anti-ferromagnetism then.
And actually the magnetic resonance work was relevant too.
We touched a little bit on the anti-ferromagnetism last time.
I think I talked about that.
Well we already touched on that last time, so letís go on and talk a little bit about it. Well we talked a
little bit about the beginning of your interest in it, but I donít think we got as far as your work thatís in the ground
state with anti-ferromagnets.
Well,let me make the connection to Japan first. There was a meeting in Maryland, I believe, was it held?
I donít remember, maybe the Naval Ordinance Lab in Maryland, somewhere in Washington, but not at the Naval Research Lab. It
was a fairly well known meeting. It was reported in the Reviews of Modern Physics. One of my anti-ferromagnetic papers,
anyhow there is some magnetism paper at that meeting. Kubo came and talked about spin waves and anti-ferromagnets also, but
Kubo had a lovely, formal way of doing it and he was estimating the energy, but he really hadnít seen the relevance to what
we would now call broken symmetry. He really hadnít realized how all of that went and he hadnít seen the relevance of the
zero point motion to the magnetization. He was just interested in producing a formal spin wave theory and estimating the
spin wave energies and things like that. So he kind of did the same thing, but he didnít think what the more general context
But he was thinking about anti-ferromagnets?
Yes, he was talking about anti-ferromagnets.
He did the same thing, but he didnít think what more general context was there.
And he was thinking about anti-ferromagnets?
Yes, he was talking about anti-ferromagnets. I think that may have been where I came to the attention of
the Japanese because he certainly talked to me at that meeting about this anti-ferromagnetic work. When I got to Japan,
also, I learned that he and Tomita had been working on the problem of exchange narrowing, and there is a fairly well known
Kubo Tomita paper which appeared just about the time I got to Japan. But I think it must have been Kubo who called me to
the attention of his seniors over in Japan, and at a later meeting, I think there was an APS meeting in Pittsburgh where
Kaya, who was then the president of Tokyo University, and Kubo approached me and said would I come to Japan. This was in
1951, very early. They said they could arrange to get me a Fulbright. That would have been the very first year that they
had Fulbrights in Japan because they only signed the Peace Treaty in 1951 so they now knew that they could get Fulbright
money for a job in Japan and they actually asked me would I come and be the first Fulbright, in physics at least. And we had
just bought a house which was very old and very much in need of repair. The furnace had had a big crack in its boiler and
all the cooking was done on a coal stove which also had a crack in it, and a few other minor things, and so we were quite
busy trying to get this house together which was much more than we could possibly afford anyhow, or thought we could possibly
afford. So I said no. I didnít even really want to go. Japan was obviously still recovering from the war. It sounded like
a very difficult adventure. I didnít know enough to realize that this was a come on rather than otherwise, so I said, ďWell,
maybe Iíll come next year and maybe only for half a year.Ē And by return mail they said, ďYouíre on. Youíre coming next
year for half a year.Ē
So I went. And by this time Kubo and Tomita had done this kind of formalization of the general idea that I had done in
exchange narrowing so we had two overlaps, two very closely related interests, both in magnetism. Iím only speculating about
the aegis of their interest in me. It was a very strange thing for them to do. After all, when they first approached me I
was two years out of graduate school, and this was a full professorship essentially, the equivalent of a full professorship.
And there were lots of better known people, I suspect they could have gotten a lot more people much more famous. Without
knowing it, Iím sure that David Pines would have jumped at the chance; he was by that time much better known than I was.
David Bohm might even have jumped at the chance just to get out of the United States at that particular time, but they chose
me and I went.
Probably because of your overlapping interests in anti-ferromagnetism.
Because of the overlapping interests with Kubo. I guess in Todai they didnít have such a very strong group
in particle physics. The particle physics group was in the Tokyo University of Education, which was when it was quite
Where was it that you went?
Todai, Tokyo University, Tokyo. There were nine essentially imperial universities, pre-war universities,
and Tokyo was the senior one of those, it still is. Then there were a number of private universities, second string in
various ways and it just happened that Tomonaga and his group centered around one of those and a good university, but not
with the reputation of Todai. And Yukawa, of course, was in Kyoto, Kyoto Imperial University.
I gather that Kubo took credit for discovering you.
Yes, much, much later. When I went back there in 1970, I believe, I had dinner with Kubo and I said,
ďWell, I practically discovered you,Ē he said, ďNo, I discovered you.Ē He had been in the states for a couple of years. He
had been at Chicago and I guess I had met him there and went always to the Chicago meeting in order to see parents, and he
came to Bell Labs a couple of times, although, well, he was gradually learning English. He never did learn English terribly
well, but eventually we got so that we could communicate well enough. But we already knew each other, in other words, when I
Tell us a little bit about response functions. This was a developing field at the time, the idea of linear
response theory. How much did you know about this and how much did you learn in going to Japan of response theory?
My thesis, as I said, was all about response. I mean, we used the fluctuation dissipation theorem without
knowing it, or I did. Then, actually, that was another interest of Kubo's, of course, and later on the Kubo formula was one
of the many results from that. And at this meeting where we were in Pittsburgh, which Iím afraid I cannot remember what the
aegis was. There was one of the big sessions in which a group of very senior people got together, sat on the podium and had
a panel discussion of non-equilibrium statistical mechanics, and one member of that session in particular was Uhlenbeck who
was talking in great length about master equations and slate equations. I guess Kirkwood was also on that panel because heís
a master equation guy. But they were talking about essentially perturbative approaches to solving the Boltzmann equation and
going down from the master equation to kind of the Boltzmann equation and all that kind of nonsense. I remember I was
sitting with Kubo, and we went out and before we actually got to talking about my going there I remarked to him, or perhaps
he remarked to me, that all of this was kind of silly because why didnít they just use the fluctuation dissipation approach
and get response functions as correlation functions of the relevant operators, relative moments and so on, and weíd been
doing all that. He, of course, had his theory of line breadths, and I had done the exchange narrowing work and other work on
line breadths, and I was very much aware of the connection. So it was rather interesting. We both knew that there was an
easier way to do linear response theory.
Iíd like to ask you more on the anti-ferromagnets before I ask you more about Japan. One of the things that
striking to me reading the paper on the ground state of the anti-ferromagnet was that he was struggling with fairly basic
questions in the definition of broken symmetry, quantum systems, fluctuation in the ground state, what it meant to develop a
broken symmetry state as you went to work in thermodynamic climate, I find thereís a notion of an infinitesimal symmetry
breaking field. Was this really the first system in which these questions were sharply posed?
As far as I know. I remember very explicitly two things. One was listening very carefully when during
that one and a half year marathon course of Julian Schwingerís, he stated firmly that it was impossible for a quantum state
to have an electric dipole moment. He said it will have various angular momentum states zero, one, two, and so on, and he
derived the restrictions for the nuclear case and the molecular case and said, ďLook, molecules donít have dipole moments.Ē
And I thought, ďThatís odd.Ē And in my other course, Van Vleck is telling me that molecules have dipole moments, and I filed
that one away. And so when I got to the antiferromagents, there was this theorem that I dug out or was given, various
literature, betas, original paper, Wallerís paper doing numerical calculations and verifying Betheís results, and some of
Wallerís papers. There was a Kramers-Kastelejn paper in which they had been trying to do entire dimensional antiferromagents
by numerical calculation. And one of the things that Waller, I guess, proved was that the ground state of the anti-
ferromagnetic Hamiltonian had to be a singlet. I checked this with Kramers and he said yes, it has to be a singlet.
Actually, I guess at various times he had waved his arms and said, ďIf you just average overall possible directions, in some
sense there has to be a singlet in there.Ē So he had some understanding of these difficulties, but he never wrote it down
But then I discovered this representation in which the zero mode, the bottom mode, was just a rigid rotor, just a
Hamiltonian of a rigid rotor. And I walked around and talked to various people and I said, ďBut people must realize these
things, people must know these things. All our seniors are very much brighter and wiser than we are,Ē people like Paulie and
Kramers and so on and so they must understand this and I found no response whatsoever. Kramers was interested in the
problem, and I think eventually he invented coherent states, or some of the mathematics for coherent states in response to
these questions I was posing to him. But eventually I derived essentially the things that are actually in the paper about
the rigid rotor, about the long time the rigid rotor would take to turn over, and that it had presumably a hierarchy of
angular momentum states. And I really had done something of a search to finds out whether anyone knew anything about that,
and as far as I know, they didnít. I donít think anyone ever did the same thing for the solid. I was aware, of course, that
basically the same mathematics applied to solid crystals. But I donít know, I guess I didnít look up the deBye-Waller
factors and things like that. I think deBye-Waller merely assured themselves that some converged at zero at the low end
and then ignored the question of exactly how it happened.
What about in ferroelectrics?
No, I didnít think about this in connection to the ferroelectric because the ferroelectric wasnít really a
One more connection Iíd like to explore a little bit. C. N. Yang carried out this celebrated calculation of
the magnetization using the Onsager solution, and if I understand this right he did this essentially by imagining that he was
going to perturb by switching on a small field conceptually. Were you aware of this calculation?
No. I guess Wannier was. He thought it was fairly miraculous. Apparently it was fairly miraculous, but
no, I was not aware of that.
Actually it might even have been published right around that time.
It probably was, yes. Wannier had been talking to me about it.
We could move fore-word a bit and letís start talking to you about your interest in NMR and spin lattice
relaxations. How did that interest begin to grow?
Well, we had beautiful cases experimentally of exchange narrowing. When the electron paramagnetic
resonance group began to — well, in the first instance, I think Charlie Kittel stimulated the experimentalist to buy a
magnet and we needed to do things with it so we needed to test samples. The first samples we tested were these things that
Alan-Holden found in an old handbook, an old Landolt-Bjornstein that we called POV because in Landolt-Bjornstein, was called
a paramagnetische organische verbindung. These were these paramagnetic compounds, organic compounds, free radicals in the
solid state. And so we looked at them, and my God, there was this enormous, beautiful sharp spectrum. These things are now
still standard in the trade because they are the best standard G-values. They have this really nice, easily measurable,
enormous single, very sharp lines. And we wondered why the lines were so sharp, so we looked up the literature and there was
this paper by Van Vleck and Gorter [?] saying itís exchange narrowing. And somebody asked me to think about exchange
narrowing and why did it happen. So that was the first, I think, almost the first thing I did.
I got involved in exchange narrowing, and then I read, of course, because Iíd been at Harvard I knew about the nuclear
magnetic resonance and therefore I read whatever Bloemberg had produced, and we were all familiar with the giant paper of
Bloemberg and Purcell and Pound, and they had this picture of motional narrowing which I think, well, again, just
qualitatively, they quantitatively described the possibility that lines can narrow because a molecule is rotating or moving
around in one form or another. And Van Vleck and Gorter had described in it terms of the moments of the line Van Vleck
always used the moment method, Wallerís moment method a great deal to estimate line breadth, and then he said in these
exchange narrowed things the fourth moment is much bigger than it should be, given the second moment. And they said if the
line is Lorenzian, then you can show that such a line has a much bigger fourth moment than it has second moment. And so I
puzzled about that, and then I figured out a way to formalize the idea that there were hidden degrees of freedom. In the
first place, why the moments worked out the way they did because of the commutation relations between the different parts of
the Hamiltonian; and the second, that you could basically think of this as causing motion in the frequency of the line
without changing intensity. So I developed a rather heuristic more or less frequency modulation model saying that the
exchange degrees of freedom caused random frequency modulation of the correlation function. So there was an exponential
decay of the correlation of the frequency without an exponential decay of the correlation of the amplitude. And then you can
show that this gives you indeed the Lorenzian line with the cut off on the tails that agrees with Van Vleck and Gorter.
Well, the physics isnít all that important, but basically it gave you a kind of a formal way of thinking about these
narrowing phenomenon, and started me out thinking about magnetic resonance in general and applying some of the things Iíd
learned about pressure broadening to the magnetic resonance problem. Most of the papers on magnetic resonance follow on from
that. The reason why Peter Weiss is on my paper on exchange narrowing was that he had done about a quarter of the problem,
but completely independently and I thought it would have been very messy for us to have published one paper which gave it all
and one paper which gave a quarter of it, and so then I suggested that we write it together.
I notice you gave some lectures on all of this when you were in Japan as well as lectures in magnetism. Just
as a side of it, in this period, what was it like to lecture to an audience that was largely literate presumably in Japanese
rather than English? You said that even Kubo was struggling with this.
I imagine that they didnít understand a word that I said.
Did you have a translator?
No, I simply gave them my books, my lecture notes. I wrote out my lecture notes in some detail and they
transcribed the lecture notes in English. Maybe they even just photostated, I donít remember. But eventually the result was
what they called the Little Red Book, of which I have some copies.
Well, I see your magnetism.
Thatís it. There were two sets of lectures. Actually one set, the notes on magnetism, were done the way I
just said. The seminar on the stochastic methods, I actually made each one of them read a paper and report on it, and they
did a fairly good job. So that was basically a seminar. I gave the first talk, and then after that I asked them to [???]
And the other people lecturing did so in English?
Yes, they did it in English, and of course they were very happy to do that because they all were working
like mad on their English. That was a very good seminar. It had many of the people who later became quite eminent in Japan.
Yoshida, Moriya, Kanimori, Hasegawa, I donít remember all the names, but they were in my seminar, not necessarily in class.
Nagamiya came up quite often for the seminar from Osaka, presumably on the bullet train, which already existed but it went
much slower than it does now.
What was your sense of that? You went from Bell Labs with its distinctive style, to Japan. What was it that
most struck you about organization Japanese physics community or science community in general?
Well, of course it was totally, totally, totally different. On a professional level it was fairly easy to
work with them. They were, of course, very competent, many of them, and we wrote some quite interesting papers together.
Kubo and I did quite of work in tandem, although I think only one of our papers was actually joint, but I was looking over
his shoulder while he was working and he was looking over my shoulder while I was working, so we had strong influences on
each other. We lived in neighboring offices and spent a lot of time back and forth. Kuboís group was very different from
most Japanese groups; it was not very hierarchical. In fact later on things got worse, and there is this tremendous pressure
for no individual to stand out(to do everything as a group and take group responsibility, and that happens even in the
science community. But that was not the case with Kuboís group. They were willing to be individuals, scientifically at
least. There was even a woman in it, which was unheard of in those days, Mrs. Ono.
What happened when we went to Japan, I got permission from Bell Labs to go, and they gave me leave for the period.
They were not yet socialized to allow sabbaticals, they gave me leave. I actually earned no credit, no seniority credit for
the six months I was there. There was a month of meeting. They had this grand international meeting on theoretical physics,
where everyone was. They invited all of the existing Nobel Prize winners, none of whom came, and what they compensated by
was inviting — I once looked at the photograph and as I remember I counted something like 17 future Nobel Prize winners in
the foreign invitees, which was on the order of 100. But it was a very flashy conference and very much not something the
Japanese could afford, but they had chosen. They wanted to do it. It was only one year after they had signed their Peace
Treaty and they wanted to do this to announce that they were now an independent power, an independent country, and they were
going to be as scientifically eminent as they had been before the war.
So I listened to a lot of talks in that meeting, and the real contrast was not in the science that was reported in the
talks, but in the presentation. Japanese presentations are still not marvelous, but they had just absolutely not realized
how to present material either experimental or theoretical. So a big difference was in presentation; not that much
difference in the quality of the science. But as you know, in particle physics, Tomonaga and his whole group were right up
with the rest of the world, but not in condensed matter, but there was good condensed matter also.
Your generation and the very nature of science in the United States have been certainly strongly affected by
the whole wartime experience. Did you find among your Japanese counterparts, people who had somehow been involved in
research? Was there a comparable impact on science in Japan?
No, not much. There had been some disastrous things, like the one cyclotron they had was thrown into Tokyo
Bay by the occupying authorities. There had been some expertise developed in radar and radio, not a lot. But of course they
had been visiting the States and they were busy taking back what was being done in the States.
Scientists, this is essentially a pre-war academic tradition that continued.
Yes, it was a pre-war academic tradition with big insertions of modern equipment. But they didnít, for
instance, have lots and lots of more surplus equipment lying around that could be immediately applied the way our people do
Having touched a little bit on NMR, I wanted to move ahead and hear a little bit about how your interest in
NMR and line width broadening led you to become interested and formulate the ideas of localization.
Thatís a fairly long way ahead. Letís see. I really have to think over life and how things went. I got
back from Japan. During the time that I had been in Japan, things had changed very rapidly in the academic world, the
academic world specifically, partly while I had been in Japan, partly prior to this. The funding system had gotten set up,
so if you were an assistant professor in a reasonable university, you had funding from the US Government and that funding was
usually through the military. So you were free to travel at will. You took MATs (Military Air Transport System). Of course
if you wanted to get to Europe you maybe went by way of Newfoundland, then to the Azores, then to some miscellaneous airport
in the back stretches of the Fens. But everyone traveled all the time. People were taking sabbaticals in Europe, having
wonderful times in Paris. Of course I later heard there were people who envied me this wonderful Japanese experience, and
they should have, because in terms of networking it was the most wonderful thing that ever happened.
So they had begun to increase the starting salaries at Bell Labs because people had been turning them down
for these very cushy assistant professorships that you can get anywhere. So when I got back there were a lot of new people
around. George Feher was there, and his salary was not supposed to be known, but I learned what it was, and it was 20% more
than I had earned when I left and it was still 10% more than I earned then, but I swallowed my pride and went to work and
worked with George Feher, went to work as more or less the house theorist for George Feher and his group. Well, I was the
house theorist for the entire magnetic resonance establishment. There was also a magnetism group that was established about
that time under Clogston with Suhl, Walker, Joe Dillon, Jack Galt. They were doing ferromagnetic resonance, and
ferromagnetic resonance had been another area that weíd all studied back in the course of this time. So I was very busy
consulting with all of these people who were doing magnetic resonance and I became interested in their various problems, and
some of the results were important physics and some were not. Feher picked up something that had already happened I guess
while I was in Japan, which was the discovery that there was a nice fat magnetic resonance that you could do on the
impurities in silicon or germanium, but silicon was now the preferred semiconductor. So you could study the shallow impurity
levels of silicon.
Bob Shulman was doing NMR, and he was interested in NMR on a various magnetic materials, magnetic oxides and magnetic
fluorides, and doing transferred hyper-plane interactions in the magnetic fluorides. There was an interesting group doing
ferromagnetic resonance of various kinds, and one theme that was picked up was the experiments of Bloemberg and Wang where
they discovered interesting nonlinear things happening in ferromagnetic resonance, which was one of the first manifestations
of nonlinear instabilities in solid state physics. And Suhl and Walker were busy learning nonlinear theory which, until
then, had not crossed my horizons, or I think any of the horizons of anyone in actually condensed matter physics.
It was an Alan Holden suggestion, and I checked it out but never published anything about it, that the key aspect of
the resonances in silicon was the hyper-fine interaction with the nucleus itself, and I estimated the size of that
interaction and came out about right. And then we wondered what the line breadth was, and it turned out we could identify
the line breadth at the interaction of the electron with the 5% of silicon 29, which was a magnetic nucleus. And again,
without actually publishing anything, I was contributing to a number of papers that George was publishing during this period.
So we became fairly skillful in studying these things. You are interested in localization. Well, first I should say
the things that should happen first. In historical order, I contributed the mechanism for the nonlinear coupling in Suhlís
study of the nonlinear affect in these ferromagnetic resonances. After that, Suhl ran with it and that was his baby. It was
an interesting thing, and as far as I know itís where nonlinearity came into condensed matter physics, as I said.
But I was puzzled. I was kind of spinning my wheels while all of this was happening. We were interested, of course,
the ferromagnetic resonance, again, was the motivation. We were interested in the ferrites and what magnetic properties
these ferromagnetic compounds might have. Earlier, I think before I went to Japan, I had Frank Stern for a summer student,
and what I had Frank Stern do was worry about the anti-ferromagnetic spin waves in a frustrated antiferromagnet. He did the
face-centered cubic antiferromagnet. And so we discovered that, sure enough, it was frustrated and unstable(even though it
was a three dimensional case and not a two dimensional case, it was firmly unstable as we calculated it. And then I wrote
this paper about frustration in the ferrite lattice because Iíd always been a little interested. Well, I wrote one
experimental paper actually about magnetite at one time, and Iíd always been interested in the complications of the ferrite
lattices, and I was interested in the magnetite charge ordering on this frustrated lattice and also the spin ordering. I
really only mention this because you two picked these things up later.
But I really kind of felt that I was spinning my wheels, and learning a lot of experimental physics, but I wasnít
really doing any big thing in theory. But then George invented this method he called ENDOR. He, of course, fought in the
1948 war in Israel, and he was originally I think a Czech and he made his way down the Danube under a load of lumber on a
barge and he got to Israel. Heís a very tough guy. Heís also, I think, a runner up in the world series of poker at one
point. He was a very tough guy in many ways. I always refused to play with George, but he made me play one game of poker
with him after I won the Nobel Prize. He said, ďYou owe it to me,Ē and I lost, of course.
At least the prize itself was not at stake.
I said there was a limit.
Well, George and Bernd and Ted Geballe, Bob Shulman, Vince Jaccarino, a number of people used to have a regular poker
game, which I did not participate in ever because these guys — I valued my pocket book. George was, of course, the best.
Bernd Matthias was the most timid, thatís the interesting thing. Heís an incredibly timid player. He never kept more than
$10 or $20 on the table.
Anyhow. George invented this thing called ENDOR which was a method in double resonance where while he was studying the
main EPR with a microwave signal, he would tickle the silicon 29s separately with a radio frequency signal, and itís a very,
very subtle and effective way of investigating all the different hyper-fine interactions. So essentially you could trace out
the wave function, or at least all the amplitudes of the wave function on all the different silicon 29s in the neighborhood
of your magnetic impurity. And we talked about it, and we worked quite a bit on how the relaxations worked.
But in the typical case of low density of silicons, essentially all the silicons were independent. The system was what
we called the homogeneously broadened. Every frequency represented a particular phosphorous with a particular atmosphere of
silicon, and the next packet at almost the same frequency would represent some phosphorous on the other side of the sample
with its atmosphere of silicon. And I was fascinated by this as a method for studying the interactions between the silicons.
The other thing we found was that if you increase the density at quite a sudden transition the line would, well, if you look
at a fairly wide range of density, you look at one side of critical density and you would see just a single exchange narrowed
line(you wouldnít see any of these spin packets). Low density you would see all spin packets. Intermediate densities, you
would see the phosphorus happen to have a spin and a half, so youíd see two lines each being homogeneously broadened. But
then you would suddenly begin to see a third line in the middle, and that represented pairs of silicons and the three lines
were the two phosphoruses up and down. And then you would see four lines, and then finally this batch would collapse and you
would have only one line. So you were watching the process of conversion of the silicon donor levels from independent local
levels to an impurity band. And there was no need for any theory, in essence; it was right there on the recording paper in
front of me. There was some kind of transition taking place. This was too close to these densities where it was still
separate silicon; weíre too close to the density where theyíd all collapse. It wasnít a gradual change from a localized to
an extended state; it was an absolutely sharp change. So I realized that almost immediately on seeing the experiment work.
George had no idea that it was surprising that his experiment worked, but it was surprising to me.
I was thinking about this. Alexei asked me about style of research and general philosophy of research, and this is one
really important aspect of my philosophy of research which I donít think young people nowadays or many people ever learn,
which is at experiment can tell you theoretical results. Experiment is often so unequivocal, so simple and straightforward
that it tells you whatís going on and tells you that some concept you had is just wrong. And this experiment was determined
to tell me that this concept of the impurity band was strange. So that was one influence. The other influence was at
exactly the same time. Kohn and Luttinger were visiting us every summer and they were doing various things, actually they
were doing things relevant to much the same set of experiments. Walter was interested in actually calculating the donor wave
functions and predicting all these separate hyper-fine interactions. He never got a perfect fit, but he could see that the
size of the wave function was more or less the way it should be.
Quin was very interested in separate experiments that were done on germanium particularly, and on some samples of
silicon where you were studying hole bands, the valence bands and the acceptors instead of the conduction band and the
donors. Because there were crossing bands and spin orbit coupling there and he worked out a nice effective Hamiltonian where
a bunch of bands were crossing and had spin orbit coupling and so on. But at the same time they were studying transport,
they were doing a quantum transport theory based on the basically the van Hove method of summation. Van Hove was equivalent,
more or less, to multiple scattering theory which had been around since the war. But they used the Van Hove way of sorting
out the diagrams to produce a diagrammatic basically Boltzmann theory of transport in metals and semiconductors and so on.
So they were interested in the quantum transport theory and in particular Quin was very puzzled by something called the
anomalous Hall affect which is an interesting spin orbit effect. And there was a theory by Smidt in Holland which could then
be shown to be demonstrably wrong, and yet the way in which it was wrong was very subtle. This anomalous Hall effect comes
out and thereís some interesting things having to do with the orders of the scattering, orders and perturbation theory of the
scattering. It turns out the anomalous Hall effect is in principle independent of scattering and itís in the order of
tau/tau, so you could easily make mistakes. Smidt managing to produce a Hall effect in the sample which was completely
separated into rows without any contact between them, and Quin was interested in that. But anyhow, I was conscious of the
problem of transport theory, and then Larry Walker described what I did as a ďcisportĒ theory, a quantum theory of non-
transport. And the basic ideas of that theory were already in place in 1956.
In September 1956 I went to Seattle where the successor conference to the Tokyo one was held. Seattle was also a very
formal, very pecking order. Since Iíd been at the previous conference I was sitting in front of the rope which had the
reserved seats in front of it, and my friend Pierre Noyes, for instance who was by that time about to become head of the
theory group at SLAC, nonetheless was sitting behind this rope. He was very bitter. I talked about this interesting
problem. I didnít really talk about localization, but about the interesting question of what happened when you cycled the
frequency through a set of these spin packets and how they can be flipped and packets could cause the flip by cycling an
external frequency through them. That explained certain effects. But I just mentioned in passing, actually the wave
functions do seem to be localized, and I think I understand that, but thatís not to be discussed here. But of course I
didnít have a theory, I had only the lowest order of perturbation theory.
You mentioned that the experiments were telling you that there were localized states there, but I gather that
many of the theorists in the community werenít so willing to take the message in the same way. Can you tell us more about
that? It was a very controversial idea to produce a localized state.
They had a perfectly good excuse because I think all of us, including me, accepted the idea that it could
be a Mott interaction that was localizing the states. I guess Mel Lax was the strongest advocate of that. Mott came around
from time to time and we talked about these problems with him, and he had his standard story where he said, ďWell, you take
the hydrogen atoms farther and farther apart and then eventually the electrons will localize on them because of the Coulomb
interaction.Ē Which was why in the paper I emphasized that the spins were also localized, and it would have been much harder
to justify spin localized states than it would have been to justify electronically localized states because there were lots
of nonlinear interactions, but there wasnít the interaction that said — It was a Z2 rather than a Z1 theory.
The point being that if it had been Mott insulator, the spin would still be delocalized.
The spins would still be delocalized. Yes, youíd have an antiferromagnet, and in fact you do have such
things in the more concentrated phases. But in this really dilute phase we could see the spins and they were absolutely
localized. One of the summers when we had everybody you ever heard of as summer visitors, that was the year we had Nozieres
and Schrieffer and Pines and Abrahams and Brockner and Huang and Lee and Brout for awhile and so on and so on and so on.
What summer was this?
Ď56 and Ď57. Pines and Abrahams came and worked, and Elihu worked particularly on the problem of how big
were the overlap integrals between these wave functions, and of course we knew the wave functions because Walter had
calculated them for us. And so he calculated what the spin exchange interactions would have been and what the hopping
interactions would have been, and they were just clearly big enough so that there should have been delocalization. But of
course itís perfectly possible not to listen to these numerical things if one chooses not to. As I will always remember,
when I finally felt that I could actually even talk about this, the response from people that mattered the most to me which
was Quin and Walter, Quinís was that itís obvious and Walterís was that itís impossible, which is fairly characteristic of
both of them. And so that was when I knew, as I told it later probably it wasnít true at the time, that was when I knew that
I had something. There was something you can differ about, and yet I knew it was right.
The method as probably you do or maybe you donít know is basically to prove that there is a convergent perturbation
theory starting with localized states. Walter and Quin had not proved but had developed a perturbation theory presumably
converging starting from the metallic end and powers of the scattering using the kinetic energy as the HO and the scattering
as the perturbation, so I said Iíll do a cisport theory with the scattering as the unperturbed energy and the kinetic energy
as perturbation, and showed that perturbation can converge. I donít know why this was seen as so difficult. There were some
games that I learned. I guess I credited everyone who helped me. Peter Wolff explained about self-energy partial summing
repeated paths. I had to learn a lot of things about graph theory that I hadnít known and then I only just vaguely used, and
then I had to learn the theorem of my own invention from line broadening theory, and thatís basically the Kolmogoroff idea
having to do with long tail distributions that you can deal with just keeping the largest term. Which I donít know if itís
ever been proved as a theorem, but itís certainly true because itís used in all kinds of places. So I borrowed the various
pieces, but then that was essentially a proof. And then nowadays when they do have proofs of localization, Tom Spencerís
proof is essentially just going through and filling in the epsilons in my original paper.
It seems that a crucial conceptual step in your 1958 paper is that random systems are quantitatively
different from slightly irregular ones, in particular that their observed rules are determined by distribution rather than
averages. How do you come upon this point of view?
Well, I had already done a lot of stuff where distributions were important. I knew that averages werenít
important because thatís the essence of the exchange narrowing problem. You take the magnetic variance of the frequency
deviation, that is no measure of the line width because thatís the Lorentzian long tail distribution. Itís even more so in
these things like what I did with Jim Talman. Itís one of the papers here, Pressure Broadening in Spectral Lines at General
Pressures, and thereís a letter. There already I was working with long tail distribution, realizing that very often the
distribution is more important than the averages. So I was prepared. It wasnít that I knew that, but I was prepared for
that idea or that concept.
The other thing which very much influenced me was just a reference from Conyers Herring. When he first heard what I
was looking for he said thereís a man named Hammersley whose papers you should look up, and he had just invented percolation
theory. So I looked him up and I actually had already known the first steps, but he certainly gave me a lot of confidence
that one could have this kind of anomalous property of random systems. So there were foreshadowings of these ideas. But you
know, itís still true that people are certain that the values are typical and that you could always do it with a perturbation
theory. Starting, well, very recently Cludie Yoshimon, I donít know whether thatís true because heís doing perturbation
theory, and thereís a problem where perturbation theory is very dangerous because itís known that conductivity doesnít self-average adequately. I didnít know the words to use for it, but I had already been thinking for quite awhile about
distributions rather than averages.
What is striking in some ways is that whereas the ??? localization itself is a crisp, complete, and
compelling argument, you kind of left the subject for many years because it seems not to have been followed up immediately
either by you or anyone else.
Several reasons. One was I just got busy. The other one was I didnít know what to do about interactions.
I thought for awhile about what to do about interactions, and it wasnít until ten years later I realized that interactions
helped, that the interacting system still had random aspects, that the Mott interactions actually tend to localize better
than otherwise. When I realized that I jumped right back in, but meanwhile there was also a slight personal problem in that
I felt a certain amount of loyalty to George to go on working with him, but on the other hand I felt a very strong tug to
work on superconductivity and I thought I had some important ideas there and I didnít really see what to do next, and he
passed this whole problem onto his student Meir Weger, our post-doc Meir Weger. Meir Weger, if you know him, you realize he
isnít the easiest person in the world to work with, and George got interested in other stuff too, so it wasnít really all
that difficult to shift out of it, but where else could one go? There were no measurements other than this one measurement
at that time and George was not going to take that up as his primary subject at all.
In retrospect, again when you came back to it later, electrical transport turned out to be a place where
hopping theory which Mott went on to develop later a bit.
(and work backwards from there(in some sense the approach that you had already taken and you were to bring
The other thing, of course, was that Mott and then Thouless brought in the concept of the conductivity, and
I hadnít realized that e2/h had anything to do with this, so it was their introduction of the conductivity that got me very,
very much interested again.
I think this would be a good point maybe to move onto superconductivity and your interest in it that you just
mentioned. So what was the defining event that got to you? Was it the publication of the BCS paper?
Well it happened long before the BCS paper, the actual paper. If you look at the BCS paper youíll find a
footnote in it that says, (P.W. Anderson has proved that this is gauge invariant.) So it obviously wasnít the publication of
the paper. Well, Leon (and that was one other name) Leon Cooper was one of our summer visitors. I donít think he was there
very long, but he certainly came and taught and he visited the institute and taught down here. I donít remember whether it
was at the Institute (one of my very rare visits to it) or at Bell, but I heard Leon.
You once mentioned you heard about his work at a Gordon conference. Do I remember that correctly?
No, thatís unlikely. There wasnít already a Gordon conference in condensed matter. The first Gordon
conference in condensed matter was the one in magnetic resonance which we organized later on.
My mistake on that.
Gordon conferences then were almost all chemistry. Anyhow, we heard Leon; everybody talked about(I donít
remember who everybody was, but everybody did talk about it and we were very interested in what he had to say. But we didnít
know what to do about it, and obviously he didnít directly explain superconductivity. There was a lot of skepticism, I
vaguely remember, on Walterís part particularly about the fact that you could very easily produce logarithmic singularities
using the Fermi surface and that very often they werenít there. Later on he formalized this with his theory with Kohn and
Majumdar, showed that impurity doesnít do anything at least to the free energy, even though if you just took the impurityís
effect on electrons it wouldnít always have a bound state. So all of us knew that this is a very tricky question and mostly
the Fermi surface doesnít appear in anything. We didnít have a formal way of saying that. John Bardeen invented his second
theory of superconductivity at the Bell Labs and I had a little experience on that because I was there in the room when John
Bardeen and Herbert Frohlich talked to each other about both their simultaneous invention of the first phonon theory of
When was that?
That was in Ď50 or Ď51. And by the time we were in Japan there was a Japanese paper more or less showing
that it wasnít true, and Frohlich was there, too, and Frohlich admitted more or less that it wasnít the theory. Bardeen was
still being stubborn as I remember that time; they were all there. Then 1956 was the year that Bardeen got the Nobel Prize,
Bardeen, Shockley, and Brattain, and although we were not invited to any of the festivities for the transistor Nobel Prize,
we were permitted to host John Bardeen in our house in Mendom. I remember that Bardeen was very much out of sorts both
because he hated Shockley and because he hated being interrupted in what he was sure was going to be the — Well, he didnít
say this, he didnít say a thing about the theory of superconductivity, but I later realized he was in a bad temper because he
was being interrupted. But thatís an aside.
I actually heard about the theory from Pines who came here to Princeton and gave a colloquium about it. I drove down
with Larry Walker and Harry Suhl and we listened to it, and on the way back Harry and Larry had been recasting the Bogolyubov
theory of liquid helium in terms of something they called spinches, which are hyperbolic kind of spins. So they said, ďWell,
hey, we could recast this BCS theory in terms of spins,Ē or Harry decided that he could. And I was interested in it and I
looked at Harryís spins and said, ďIsnít it interested the electronic state in terms of Harryís Spins looks like a domain
wall,Ē and left it at that for the time being until that next summer. That summer Gregor Wentzel came around to the labs and
gave us a couple of lectures proving conclusively that it couldnít be the right theory because it wasnít gauge invariant, but
by this time Iíd already convinced myself it was the right theory because it was another case where experiment tells you what
the theorists donít. There was no question the experiments were so completely explained. All kinds of experiments. So it
had to be gauge invariant.
I used to spend days at home and we went walking up at the local hill which was called Bald Back on a beautiful late
summer day and lay there in the sun and realized that what was important was there was no order parameter here and these
spins could rotate around that way, and that somehow I had to derive the theory of the appropriate waves and set out to sort
out the whole problem of collecting modes in this theory.
And there was a lot of other stuff. There was a point that you had to separate longitudinal from transverse
excitations; then I realized that there was a coupling with plasma modes, and I wrote a very incoherent first paper which was
the Phys Rev 110, 827 paper, and thatís what Bardeen was referring to. It does more or less what it says it did. It
explains that there is this longitudinal-transverse separation and so on, but it certainly didnít have the formal ideas
worked out. And then I set to work to calculate and calculate and calculate, and that was this new method and the random
phase approximation. Thatís where I really calculated the collective modes using the random phase approximation, the
equation of motion method that Bohm had used for plasmons, showed that if you generalized that it gave the long wavelength
spectrum of the BCS theory and had the Higgs phenomenon in it, although nobody called it the Higgs phenomenon yet, but I
showed that that was okay, that in this case there werenít spin waves, there wasnít a collective mode.
So your realization that there was no order parameter to that would be the summer of Ď57.
Yes. Well, there were various other things in that original — I donít remember exactly what, I just
remember that I came down with a very happy feeling that I was going to solve this.
So your next paper in the sequence is the theory of dirty superconductors and the sequence of
Yes. Well, thereís RPA.
Right, which you mentioned, and the new method and the next two things you do in superconductors are dirty
superconductors and the case of the Knight shift.
Yes, those are basically impurities. Thereís a lot of stuff having to do with impurities in
superconductors. I did everything but do the right theory, which was Abrikosov-Goríkov. And Harry Suhl was working in this
field at the same time; he also had jumped into superconductivity and working with Matthias thinking about magnetic
impurities in superconductors.
But actually the theory of dirty superconductors was — You have to go back — How did I get to California? That was
one of the three things that all happened in California during that summer. Back in here, one of the papers we went past was
called Cyclotron Resonance in Metals. I guess I talked about this a lot with Alexei, so I donít need to go into detail. But
anyhow, that involved Charlie Kittelís being spitting mad at me for having tread on the toes of his group, his collaborator
Kip and his group, who were doing cyclotron resonance work in metals, and he said itís wrong and whatís more you stole it
from us and so on. Yes, he spent an hour and a half on the phone and I just held the phone over there because I didnít have
the faintest idea what he was angry at and he had nothing to be angry at me about anyhow. I had just been trying to explain
to Jack Galt, who was doing measurements of cyclotron resonance in metals, that his data couldnít possibly be the
straightforward thing that he thought they were because the straightforward thing he thought they were was a very dull,
smooth structure. Then the more closely you examined it, the duller and smoother it looked.
But I didnít explain Galtís effect. I felt very guilty about that because Galtís effect did turn out to be a very
interesting piece of work. He was seeing the Azíbel-Kaner resonances in a rather difficult regime in which to interpret
them, but they were very relative to fermiology and the bismuth samples he was looking at. But I didnít have the foggiest
idea what they were; I just knew they werenít this straightforward cyclotron resonance effect.
Nonetheless, I was glad enough to be frightened off the whole fielded by Charlie and I had these other things to do
anyhow. Charlie obviously felt guilty about this. It seems a strange thing for Charles Kittel, if you know him, that heís
capable of guilt, but he must have been capable of guilt [laughter] because he thereupon invited me two years later out to
California. Dyson had spent two years visiting him in the summer on his Union Carbide grant that heíd gotten especially for
Dyson. He had another year of it and Dyson was off designing hydrogen bombs or hydrogen bomb driven rockets. So Charlie
invited me, which was a great honor. He secured me this wonderful house 800 feet up the hill next door to the Rad Lab and it
was about 150 feet long and had a porch all along the front and a beautiful view which we saw for exactly two days until the
fog rolled in, but it was a very beautiful place and we had a wonderful time.
Jim Phillips was post-docing with Charlie at the time. There were three students, Phil Pinkus, Ray Orbach, and I
forget who the third one was, and I was supposed to take care of these students and spend time with Jim. The theory of dirty
superconductors ďJim and I were walking around the campus one day and he said, ďWhy donít impurities effect superconductors?Ē
And I thought for about a microsecond and said, ďI suppose itís because of time reversal invariance,Ē and then I thought for
another considerable number of seconds and I said, ďWell, I can fix that. I can do that.Ē And so I invented this kind of
scattering representation. I donít know that youíll actually find it anywhere in my previous work, but it was somehow a
little bit in the back of my mind. Exact impurity eigenstates. If you put it in terms of exact impurity eigenstates it
becomes trivial and obvious. And so that was the reason why that happened in California.
Can I ask a question just out of sheer curiosity? Why the Journal of Physics and Chemistry of Solids?
It was new at that time and it seemed like an interesting place. I didnít think it was a very important
paper. It was that new journal, and I wanted to encourage them, but thatís not a particularly important paper. But that
delayed its publication for a year and a half because they had troubles with their printers.
Then using the same method for the Maxwell skullduggery night shift was fairly obvious, except that you had to also
express the magnetic resonance line shape in terms of the scattered wave functions in the presence of Elliot spin orbit
scattering, and then you saw that basically the fraction of the Knight shift that was only the gap relative to the total line
width would be killed by superconductivity. A very simple argument. There were wrong papers before that, but that was
actually the correct explanation for the fact, which had been very much publicized but never bothered me much, that the
Knight shift came out finite in most small particle samples of superconductors.
The second thing that happened in California was I went and listened to Leslie Orgel talk about the theory of local
electric fields on transition metal atoms and the splitting of orbital states in transition metal atoms, and realized that
that was a way to quantify the wave functions for transition metal atom electrons in Mott insulators. And at the same time I
think Iíd already had the germ of the idea that super-exchange was due to the Mott insulator effect, but I hadnít known how
to do it quantitatively and I listened to Leslie Orgelís series of lectures just out of idle curiosity and they said,
ďWonderful, I can actually do the whole quantitative theory of the wave functions and their overlap integrals and super
exchange.Ē And so thatís a result of being in California that summer.
The third was I was there when Charlie got a letter from Russia saying that he was to organize a delegation to go to
the all-union conference on dielectrics. He hadnít been with the first group that went the first group after the thaw. His
colleague Kip had gone and I suppose thatís when he was asked to the second group that went to Russia.
Now this was the summer of Ď58.
The summer of Ď58. We didnít have much time, but it was December of Ď58 that this meeting was and I said,
ďIíve got this old work in my notebooks, I can talk about that. Iíll go.Ē So we were the second delegation of solid state
physicists to go to Russia that winter. Again, I ascribe this to Charlieís serious feeling of guilt, and I do think he also
thought it would be great to put me in contact with the Landau Institute, of which Iíd practically never heard. I had no
idea that they were who they were.
Incidentally, one of the things about the Bell Labs that you need to realize, Abrikosov, Goríkov and Dzialoshinskii,
the thermal greens functions did not come as a surprise to the group in Bell Labs because one of the things that was done
during this summer was that Ward and Montroll developed, essentially, the identical formulas at the same time during their
summers at Bell Labs for those two summers, Ď56 and Ď57. There were also Schwinger and Martin, but Wharton Montroll was
perhaps more complete than Schwinger and Martin.
Actually, thatís generally not in the literature. Schwinger and Martin are characteristically credited
But itís published with —
I meant the referencing.
Yes, itís not referenced, but itís published.
Historical note here, the Matsubara frequencies did come by AGD.
Now, tell me about that then.
Well, they were doing it exactly the same way. They invented the frequencies for themselves. The
Matsubara frequencies, itís not clear whether Matsubara or Kubo or both are responsible for them.
When I asked the Russians about this, they said itís not in Matsubaraís papers at all, actually, so the
Russians claim that they discovered it independently and couldnít agree on who to name it, so they put Matsubaraís name on
the frequency, but thatís the story Iíd heard from Goríkov because Iíve just heard your end of it.
Thatís interesting because when I was in Japan in 1954, Ď53, Ď54, Kubo had already invented the periodic
imaginary time coordinate and I said, "What use is that?Ē One of the cases in which I really was notoriously wrong about
something. [laughs] I said, ďThatís just formalism, for Godís sake.Ē Yes, Kubo actually is the discoverer of the —
Thereís the Kubo, Martin, Schwinger condition.
Yes, and that was in 1954 and he published it shortly thereafter. So we were talking about that already
before I left Japan.
There is one more paper on superconductors from around that time with Harry Suhl on spin alignment.
Yes, Suhl had already done his paper on impurities in superconductors with Matthias where basically he had
taken the theory of dirty superconductors, he hadnít taken that, but itís the same idea when your impurities are not time
reversal invariant. He actually, I guess, did it from the point of view of spin susceptibility. He said the spin
susceptibility of the superconductor is zero, and therefore the free energy doesnít have a term proportional to M squared and
therefore the free energy of the normal state will be lowered relative to that of the superconducting state. So he could
estimate where the critical amount of scattering would reduce the transition temperature. This did not give you the right
behavior at the transition temperature at all. It wasnít the perturbative way, it was just a variational comparison of the
two energies, and Harry never really sorted that out.
But while he was working on that, we began to think about — Well, Bernd had been doing a lot of work on impurities in
superconductors and heíd found what he called ferromagnetic transitions. Now Bernd Matthias doesnít know a ferromagnet from
a hole in the ground; heís not at all interested in order parameters, symmetries; he couldnít be less interested in exponents
and critical points. He just saw that there was some kind of phase transition there and that it tended to cross the
superconducting phase transition and funny things happened below. And we tried to interpret what was happening there. Itís
quite a wrong paper. Well, not wrong, but itís quite a naÔve paper about this problem, but itís interesting because itís my
first brush; it left a trace in the memory of the spin glass because these things that Bernd was seeing ferromagnetic
transitions were the actual spin glass transitions.
Now I want to just go down the list of your papers to pick one out because itís connected to the work of
superconductors that weíve been talking about, and thatís the one on plasmons and gauge invariance and mass from 1963. Now,
in that paper you actually discussed this business of the Anderson-Higgs mechanism, but in terms of some work by Schwinger.
Which I had not read at all.
Which you had not read at all because you tagged somebody else for bringing that to your attention. In some
sense, by the time you come to that, in your paper, essentially, you say in as many words that this Yang-Mills goes on in
roughly equal —
No, itís completely the Goldstone boson.
Well, you have in there both the idea that the masslessness of Yang-Mills, you say explicitly, can be killed
up against the masslessness of —
But the masslessness of Yang-Mills comes from the masslessness of the Goldstone boson, which was already
there in (phi) fourth (to the fourth power) theories and such theories, or any theory with broken symmetry.
Now, how did that happen? During those years, actually — I should have said, incidentally. I never said even to
Alexei that for the first two years of the theory group, Conyers ran it; the next two years, I ran it. Then when I left to
go to England, Lax took over. So I was, except for that summer of Ď58, actually organizing these summers, but really it was
all a collective bit and it was Peter Wolff who kept us in contact with the world of particle physics. We had quite a number
of particle physicists buzzing through. Ward, of course, because he liked to come and work on engineering because heís
manic-depressive and if he would work for too long at particle physics he would go into his depressed phase. Well, itís not
funny, it was very tough for him, so he would come around and work with Larry Walker and John Pierce on electron tubes for
a-while and he would get out of his depression and have to go back.
Funny that he had to tackle with the idea that if you were depressed, you wanted to go to Bell Labs.
Yes, he was depressed and wanted to go to Bell Labs, which was strange. Then there was John Taylor who
came around and we talked. Well, Brueckner was around a couple of those summers as we will learn shortly. Wentzel of course
was earlier. He was a friend of Berndís when he came around during those first couple of years. So we had contact with the
particle physicists. I met some of the particle physicists in Cambridge also later on in Ď61 when I was there. Jeffrey
Goldstone was there, and Steve Weinberg was actually there in Ď61. I talked to him in the tea line every once in a while.
But from the students I learned that they had this trouble with this Goldstone theorem and I said, ďI can fix that.
Goldstone theorem doesnít hold in superconductors.Ē So it was only after having heard of the Goldstone theorem I wrote this
paper to say Goldstone theorem, schmoldstone theorem. Itís okay. You donít have to have a massless particle.
Nambu came visiting. Nambu actually was very useful in helping kind of grow up my thinking about broken symmetry. I
realized that it was a general phenomenon and that it could happen in particle systems and he came to the labs and talked
about his lambu Nambu-Jona Lasinio paper before it was ever published. So I had a lot of contact with Nambu. Of course he
was using the Goldstone boson for his pion, but then they said, ďWe want to make theories in particle physics, but we havenít
gotten enough massless particles,Ē and, as I said, I realized I could fix that. So I wrote this paper and it was published
in the Phys Rev rather to my surprise and nobody paid any attention to it, much.
Then unfortunately I heard about this early work of Schwingerís and referred to it, but it had absolutely nothing to do
with my line of thinking. I donít know whether itís right. I suspect it is right. Itís kind of a general, very general
argument that thereís no particular need for a Goldstone boson rather than a specific model that will give you the Higgís
mechanism. And then there are things in the paper that are not in Schwinger at all.
But, yes, I knew what I was doing. And the reasoning came out in Ď63 is simply that I just sent it in as an ordinary
paper and they had about a yearís delay. I donít think there was refering delay. I wrote it in the summer of Ď62 after I
got back. I was also doing some other things that summer.
I guess the thing I want to get to is this sort of modern understanding is in terms of the statement that if
you have a system when symmetry breaking would normally produce the Goldstone boson and you have a gauge field, a Yang-Mills
field, in general, that the combination of the two —
Well, we didnít know about Yang-Mills fields, really.
Well, in your paper you actually do have the word.
Do I say Yang-Mills? Yes, I think some of the young people at Cambridge had explained that to me.
You in fact used the words "masslessness in Yang-MillsĒ because that was a problem that was obviously there
starting from the end of this paper.
So, clearly by Ď63 your formulation is actually pretty much contemporary. What I was curious about was if
this happened as a result of your interaction with particle physicists at Cambridge that you kind of went—
No, particle physicists at Bell more than at Cambridge.
A formulation from the early superconducting work.
Yes, and particularly John G. Taylor. I talked a lot with John G. Taylor, but there were also other
people. Well, I talked a little about super exchange, not much. I guess enough.
My thought was that we could do helium three and then tend to local moments afterwards. After sort of
looking where the synthesis in broken symmetry came around and you wrote this book **Concepts in Solids.
Yes, helium three comes before Josephson, doesnít it?
And thereís super-exchange.
The super-exchange must have been in Ď58.
Well, the theory occurred to me in the spring of Ď58 and I was working on it in the summer of Ď58 when I
heard Orgel, and then a lot of stuff that went into the paper was due to the fact that Bob Shulman was simultaneously doing
these transferred hyperfine measurements on — Well, KMnF3, KNiF3, the fluorides where you could do hyperfine measurements on
the fluorine. We didnít have a transfer of hyperfine on the oxygen so we could really very quantitatively estimate what was
going on there, but that was not a consequence of the experimental, but it was very nice to have it go
experimental/theoretical at the same time. Bob and some of his collaborators were very helpful.
November 5, 1999
November 5, 1999 for the third of our discussions with Phil Anderson and his career. Weíll take up today
with his work on superconductivity and preferably also get to some work in local moments. So the recent Nobel to Veltman has
brought him to focus again the Higgs mechanism which we talked a little bit about last time, the fact that it was invented by
you before Higgs came along. Would you like to elaborate a little bit?
Well, there were a couple of things that I skipped over. I think I skipped them over in both of the sets
of interviews Iíve done. One of them is that during this period I was in fairly close contact with Bob Brout. Later on, one
of the co-inventors of the Higgs mechanism is Brout with Francois Englert. Bob spent several summers with us down at Bell
and I know that I talked many of these things over with him. So he was definitely one of my sources for knowledge about
particle physics, along with John Ward to a much, much lesser extent.
Therefore, when I was recently helping edit one of the accounts of the recent Nobel Prize and noticed that they
ascribed the idea, they call it Higgs, Brout, Englert, which Iíd never heard, I realized that actually Brout and Englert had
a fairly considerable influence on the whole development(must have gotten their ideas from me. So I had thought that it just
fell into a black hole and Higgs reinvented it and everybody called it the Higgs mechanism because of that, but in fact, it
is in the linear chain of what eventually led to tí Hooft and Veltman. So I was quite happy with that. I guess the
intellectual strain is I was working on, of course, on superconductivity alone and then Nambu came to Bell Labs and talked
about his work with Jona Lasinio in which he invented basically the idea of symmetry breaking in particle physics. So I
became aware of the possibility of symmetry breaking in the vacuum and Nambu directly applied the ideas of BCS to the problem
of the nucleons and the pion.
But there was a lot of worry, a lot of fuss going around, and I talked briefly with Brout, with Nambu, with various
other people about the existence of the Goldstone boson which was my old antiferromagnetic spin wave and the Bogolyubov in
superconductivity, and I realized that this mechanism eliminated the Goldstone boson and replaced it with a massive
excitation which eventually I realized was itself a boson. Then from that point I basically understood the Higgs mechanism
even in the context of superconductivity. But I think I was encouraged by both Brout and by John Taylor to write it out in
explicit form, so I finally wrote this paper up which I submitted in Ď62, which does seem, looking back at it, to embody the
Higgs mechanism in rather final explicit form. And itís a new discovery; it is, in fact, in the main line of development of
particle physics, which I had not realized.
So I want to move onto other things. Clearly throughout the 60s you were deeply engaged in various aspects
of phenomenological superconductivity. The first thing I wanted to take you back to is a set of papers you wrote, I guess
with Pierre Morel, on the possibility of paring in helium three from 1960, Ď61. Could you tell us something about them?
Well, actually in my notebook youíll find a very, very early but essentially correct discussion of the
possibility of finite angular momentum of BCS states. I just wrote this down as a curiosity and was stimulated to do it by a
man, an unknown character named Fisher, who was in the metallurgy group at General Electric and who came to, I think, the
Geneva meeting or one of the early meetings on superconductivity, a post-BCS meeting, and maybe he even gave a talk about
this idea that the BCS gap could vary on the Fermi surface. But he had no idea that it should be sorted out in angular
momentum quantum numbers, which I then arranged fairly straightforwardly in this work that I put in my notebooks.
Brueckner was one of our many summer visitors to the labs, and he dropped around to my office and told me about the
existence of liquid helium three, which of course was being studied at Los Alamos predominantly because it was the decay
product of tritium, which is of well-known importance in nuclear armaments. And John Wheatley was just beginning to study
helium three at the Los Alamos labs, and the Landau paper, of course existed, but I wasnít aware of it, talking about the
Fermi liquid and the possibility that helium three was a Fermi liquid. Brueckner said, ďCould this possibly be one of your
aligned angular momentum states on your orbital angular momentum states?Ē And I said yes and set Pierre Morel, who had come
to me as a student, to do a formal theory and do a better theory of it.
We looked at the interactions, and the very primitive interaction estimates that we could make at that time suggested
it certainly couldnít be what is now called an S-wave. It could be either a P-wave or a D-wave. So the first part of this,
Pierre was all ready to publish when we heard from Brueckner that he and his student Soda were about to publish the idea. I
called up Brueckner and said, ďHey, I have a graduate student on it too and it was my idea and I do think itís unfair for you
to publish it all by yourself.Ē So he modified his paper slightly and I added a little bit to it and so you have this
peculiar list of authors, Brueckner, Soda, Morel, and me.
And why does it have level structure of nuclear matter in the title?
Oh, he was also suggesting that this kind of thing could happen in nuclear matter, which was, I guess,
where he got on. Actually, he blew that one because I had suggested to him very early on that the BCS theory might apply to
nuclei, and he said, ďNo, no, no, no. Thereís nothing like that in nuclear physics.Ē And so Pines and Bohr and Mottelson
submitted it a few weeks later after I made this suggestion. So he owed me one. He was glad enough to add my name on that.
Basically, I put it off on Pierre and quite correctly because Pierreís career might well depend on his being on this.
Then Pierre and I set to work and really did a proper job of the formal part of the theory and it was in that paper,
and I donít remember exactly which of us, but I think it was in discussion with the two of us that we made the really
important discovery, which is the discovery of multiple phases in the superconducting state, which, of course, was the way in
which you identify helium three almost immediately when it was finally discovered experimentally. The way in which you
identified it is that itís very likely a higher angular momentum state because of the existence of the two phases, the A and
So we discovered the physics behind this multiple phase structure which has, itís still a very important aspect of the
various proposed higher angular momentum phases in such things as uranium platinum three, uranium beryllium 13, and so on.
And that is a very characteristic thing and comes about because the angular momentum separation is adequate for the linear
terms in the free energy cell, the quadratic terms, linear terms in the response functions. But the higher terms in the
response functions donít satisfy simple angular momentum group theory because itís not a linear problem. They are non-linear
in the angular momentum group theory, so you have to do the group theory in a more sophisticated way and realize that the
quartic terms in the free energy will divide out different phases from each other. So this was the real discovery of that
The other was duplicated by a number of other people independently. I donít think anyone realized this multi-phase
structure until much later, and it was from the multi-phase structure that Balian-Werthamer went on in 1963 and Tony Leggett
in 1965 to produce improved theories of helium three.
Since Kyoto and Seattle, when I had been very young and rather obscure, the first really big international conference
in which I felt I played some real role was the Utrecht conference. Basically it marked the moment in my mind when particle
physics and nuclear physics and condensed matter physics were all really talking about the same thing, and there were
representatives of all those fields at that conference and we were all talking the same language. Jerry Brown, for instance,
was very active there. Youíd find Kerson Huang sitting in the first row of the conference photograph. T.D. Lee was there,
and various eminent particle physicists. A few Russians, but the Landau group was not yet free to leave Russia.
And I decided to go for it and this helium three thing was, of course, a complete gamble. So I chose to talk about the
helium three theory at Utrecht, although I had plenty else to talk about. I could, I suppose, have talked about the Higgs
mechanism, but I didnít. I decided to gamble and talk about helium three and of course that was the source of many contacts
that had different consequences. One of my good friends at the time was Bill Fairbank. I had just been to Stanford studying
an offer that I had from Stanford and had gotten to know Bill Fairbank who was the team experimentalist at that conference.
Bill Fairbank and Cor Gorter had an interesting conversation when we later visited Gouter where they both talked about their
efforts to discover flux quantization. As you know, Fairbank won; Gouter had the wrong idea. Fairbank knew why it was the
wrong idea, but he wasnít about to tell him why it was. He told me later on why it was the wrong idea. Gouter was trying to
do it with a loop and Bill Fairbank realized what you wanted to do was separate the charge quanta that are at these opposite
ends of the solenoid, get them as separated as far as possible because that would make them easy to detect.
But anyhow, Bill Fairbank and I had a very interesting time. We wandered around Amsterdam together, visited the famous
Red Light District, which was kind of a disappointment with Bill because heís a very straight laced, fundamental Christian.
He talked very nicely to the ladies, but we didnít use their facilities in any way.
As physicists, you felt compelled to explore the infrared.
I actually have a semi-technical question about this. Helium three is an unusual system in that most of the
time when one is doing many-body theory, you donít really have a hope of getting the microscopics particularly carefully, and
so one is really proceeding on the basis of attempting to identify the correct broken symmetry or something. This is a
problem in which you could hope to do essentially something approaching an abin [?] issue. How much were you worrying about
these sorts of things when you were developing a theory? Was this something that was in your mind, that this was in some
sense a test period?
It was definitely on Bruecknerís mind, but I felt that Brueckner was being over optimistic. I thought that
he was really quite naive in feeling that whatever interactions there were werenít going to be terribly renormalized. We
knew what the interactions were. Both of us agreed that the interactions were reasonably well calculable and were available
in the literature of the 30s, in fact. But I felt he was over-optimistic in approaching the thing from that point of view.
Later on with the development of the theory of the nearly ferromagnetic spin fluctuations by Berk, Schrieffer, and
Doniach, we began to realize why it was that our very crude estimates of TCs were very, very wrong. If you took the Berk,
Schrieffer, Doniach ideas seriously it was clear that the D-wave TC was going to be in the ten to the minus ninth range and
you were never going to see it. What we didnít realize was that there was an attractive term from the spin fluctuations that
would make the P-wave transition temperature higher. That was actually discovered by others. It was suggested by Emery and
calculated out by two guys at Stevens, Percus and Yevick. That was ten years later, but we knew that at that time we were,
even if we knew perfectly the interactions, very far from being able to figure out what the true renormalized interactions
were going to be, and that took a long development. Even now people havenít really done it right, as you know.
So letís skip a little bit ahead to keep this continuity of your work in superconductivity. I think the next
papers I find, you have a paper with David Thouless in the diffuseness of the nuclear surface. Is this conceivably
No, this was just because David Thouless was in Cambridge at the time and we were interested in collective
modes and nuclei generally and you had the new idea of collective modes of these fluids. David and I, for some reason or
other, were talking about the surface collective modes and we decided that we could calculate surface collective modes and
find out how diffuse the nuclear surface was made by that, but it was just an incidental calculation job.
So I think the next thing is then the theory of flux creeping in hard superconductors.
Weíd better do the Josephson effect before that.
Please, go on. I was simply following the literal bibliography.
Well, my work on the gauge invariance and on the random phase approximation made me conscious of the
existence of collective modes in superconductors and gradually the ideas of Ginzburg and Landau and Abrikosov about how
superconductivity accommodated magnetic fields and so on began to penetrate the west. From these two points of view, I
became conscious that there was a Ginzburg-Landau theory and there is an order parameter in the superconductor and so on.
So I was gradually developing the general idea of broken symmetry in the back of my mind. I started from the antiferro
magnet, where I had first seen this concept of quasi-degeneracy, although I didnít call it that. Then Nambu introduced the
idea of broken symmetry into particle physics, and I think it was from Nambu that I first heard the word quasi-degeneracy,
and I resonated to words which he used which were distinct Hilbert spaces. He said the thing about the different vacuums was
that they represented distinct Hilbertís spaces and they were non-interfering because they represented very small
displacements of a very large number of effective variables.
At this time I went off to Cambridge and the story of Cambridge, well, I had been there—
What year was this?
Ď59. Well, the first time I had been to England since 1937 when I was there as a kid, the first time Iíd
been back to England was 1959 and Joyce and I spent a little while wandering around England and we enjoyed ourselves with
Susan very much. And then both, it turns out, Roger Elliot, whom I knew from various things in magnetic resonance, and Brian
Pippard, whom I knew from the meetings on superconductivity that Iíd been to, approached me to go to England and spend a
sabbatical year there.
Roger, I guess, was first. He wrote me fairly formally and I said, ďWell, Iím interested,Ē and then Brian Pippard
spoke to me at the Toronto International Low Temperature Meeting. I guess Roger was there, too, and I asked him one
question. Iíd heard about the peculiar teaching systems that these universities have and I said, ďCould I give a lecture and
would anyone come and listen?Ē And Roger said, ďOh, no, you donít need to do that,Ē which the implication of which was very
obvious. And Brian said, ďGee, that would be great,Ē essentially, although Brian never said, ďGee, that would be great.Ē
Brian said, ďWe would very much enjoy having you do that,Ē in very formal English fashion.
And so I made the decision to go to Cambridge. Brian and Neville Mott fixed up with the new Churchill College that I
would be invited and be one of their first overseas fellows, a new status that Churchill College was just then inventing. I
didnít know that this was an extraordinary honor or anything about it. I guess there were three people who were very helpful
in this whole business, David Shoenberg, Brian, and Neville, and all of them had seemed for different reasons to be very
positive about my coming.
I wangled an arrangement with Bell Labs, which actually was very satisfactory. This was one of the few early
sabbaticals which set the format for similar sabbatical arrangements later from Bell Labs, but there was no difficulty with
it, and since they continued my salary at, I think, a roughly 25% level, my salary from Cambridge was essentially equal to my
salary from Bell Labs and I lived very well and very comfortably. And so we went off to Cambridge and I did lecture. The
lectures later became the book Concepts in Solids, which was full of the ideas that I had been kind of developing, ways of
thinking and talking about the next side of physics that I didnít think were the conventional ways and possibly might be
useful to students. Toward the end of that course I mumbled a little bit about these ideas about broken symmetry and I had
the ideas of orthogonal Hilbert spaces, the idea of quasi-degeneracy, the ground state, the idea that there was an order
parameter in the superconductor.
In doing this whole lecture course Iíd had Brian Josephson in the class and I knew who he was for two reasons. One was
that in my magnetism half I knew Walter Marshall fairly well and Walter Marshall was fond of telling the story of Brian
Josephson and the Mossbauer effect. I forget which group was getting the right answers for the Mossbauer effect because in
England they were doing things at room temperature, which was just as cold as the outdoors, whereas I think the American
group was allowing the photons to fall from outdoors to indoors. Therefore they had a relativistic thermal shift. The
relativistic thermal shift was calculated and proposed by Brian Josephson, who was then an undergraduate, and Walter Marshall
loved to tell of calling up the porter at Trinity College and asking for Dr. Josephson and the porter saying, ďWe have no Dr.
Josephson here,Ē and he kept probing and said, ďOh, him. Heís an undergraduate.Ē And they called him to the telephone and
Walter talked with him. So he then was already well known to be brilliant.
Anyhow, he was in my course and every once in a while I would slip in one of my blackboard derivations and he would
gently point it out to me after class, so I was aware that he existed. He was a graduate student already at this time of
Brian Pippard working on superconductivity. It was an interesting exercise in rather hard work to achieve not particularly
exciting outcomes, but he sat at the tea table with the rest of us occasionally and we talked about various things in
superconductivity, or the group talked about superconductivity.
He came up to me after one of the classes and handed a sheaf of papers and asked me to look through these papers. He
thought he had found a way in which the current in a tunnel junction would depend on the phase of the superconducting order
parameter, and he said heíd become interested in the question of the phase because of my comments in class. This calculation
was a real mess because he had insisted on sticking with the original BCS notation and keeping track of the numbers of
particles in explicit detail. So it was a miracle that nonetheless he managed to introduce a phase and discovered that there
was a dependence on the phase.
Fixed particle number states?
He was working with fixed particle number states but he kept the N and N plus two states on one side(
But he kept the N and N + 2 states on one side and the N and N +2 states on the other, so he realized that
he could somehow measure the phase. He did this because he wasnít sure. I think he had done it at first the right way, but
he wasnít sure that people would accept it. Anyhow, I read through this thing and he had four separate terms and I only read
one of the terms and I said, (I canít see anything wrong with it,Ē and from that point on we discussed this and he came to
the [???] often and we discussed it at length. We didnít really understand totally what the interpretation would be. Now
Brian Pippard claims that I was the first one who said, ďOh, I supposed itís really a current proportional to sine phi.Ē The
expression that Josephson had didnít make that explicitly clear. So according to Pippard, that as part of my role and part
of my role was just to say, ďWell I was really persuaded...Ē talking to the convinced I guess in Josephsonís case, but I
certainly persuaded Pippard that it was all right that there was a phase and that this was a thing that one could calculate,
one could expect due under physical results.
Aside from that I didnít have much of a role in what Josephson did, except to say, ďYes, itís real. Itís fine. And
itís important that it is actually an explicit way of measuring the phase of the order parameter, the important constituent
in the order parameter.Ē He was responsible, for instance, for finding the tiny little bit of Gorídov derivation of Landau
Ginzburg that said that the phase varies with the i mu t, in other words, the Josephson relation for the frequency, which
Josephson cribbed out of Gorídov, but it had no prominence in Gorídov at all. So he realized that it was going to have this
frequency dependence, entirely independently. He realized how one could measure the frequency dependence with the driven
nonlinear effect. And he had the right dependence on the penetration depth. I later re-derived that and got the wrong
answer and sent it to him, and he wrote back and said, ďYou have the wrong thickness in your dependence on magnetic field,Ē
and sure enough he was right.
So almost all of the actual phenomenology of the Josephson phenomena was entirely invented by Josephson. He was
brilliant in those days. He really was fantastic. I mean inventing the synchronization of the Josephson current in itself
would have been a major discovery by someone else, but he first discovered the phenomenon and then he discovered how to
measure it. Most of the phenomena then were entirely his discovery and he wrote it up. He still was fixated on Cambridge
and fixated on Trinity College and he wrote a letter and Pippard was still dubious enough about it to insist that he send it
to the Physics Letters and not Phys Rev Letters, and partly also it had to do with [???]. Cavendish didnít want to spend
money on publication charges. But then he did a full theory complete with the idea of and the fact that with the current
there was an accompanying energy, and essentially what I later published in my Ravello notes, he wrote all of that out in a
scholarship thesis for Trinity College of which he made three copies, one of which he claims he sent to me but I actually do
not have it and I would have it if he had ever sent it to me, so I have no knowledge of that scholarship thesis. And another
one to Pippard, but he didnít publish it.
So here was this letter and this wonderful thing. And as soon as I got back to Bell Labs, John Rowell was doing
tunneling experiments following on from Alan Chynoweth who had started the program doing superconducting tunneling
experiments, and I said to John, ďYou must look for a glitch near zero voltage, because there is this term that Josephson has
derived and heís derived it correctly itís really there and we donít even see why you donít see it.Ē And John, with each new
batch of junctions he would look, and that fall about in the month of November, he had a new batch of particularly low
impedance with a particularly thin oxide layer, and he discovered, he saw the glitch and we worked a little bit on that and
brought it up to the point where we could actually observe it. Then I wandered around his laboratory with a little
refrigerator magnet on a string and we watched the current fluctuate as we went and waved this refrigerator magnet around and
we realized that it was very, very sensitive. This was when I wrote Brian and said, ďWe found that itís very sensitive to
field,Ē and I estimated, well, I wrote him the whole story as to what weíd seen and I estimated that itsí sensitivity to
field was a little high because there wasnít enough field in the distance between the two layers. Brian wrote back to me and
said you should have used the penetration depth for that distance, which I had already realized independently, but he
So I sat down seriously to think about the Josephson Effect and why it as so difficult to observe, and in the course of
the next week or so, I reproduced this thesis of Brianís, the energy argument and so on, and essentially the essence of that
is published in this letter with Rowell. And of course the problem had been that John Rowell did not have a screened room to
do his tunneling experiments. And there was a lot of noise around the laboratory. There were spark cutters and noisy
machines of various kinds. There was a lot of noise coming down the mains lines into the cryostat. So the effect was very
much diminished by noise. When slightly later John was able to get himself a screened room, he could make really accurate
measurements of it. Later on Giaever and various other people claimed that they had also seen the effect. I repeated that
in some of my articles later, review articles about it. I was wrong. Talking with Bob Dynes, we looked back. We found that
John Rowell was working with lower resistance junctions than anyone else could possibly have been, that Giaever when he
claims to have seen it as working with a junction that was in the meg ohm resistance area(he would have had no possible way
of seeing it in the presence of even thermal noise and of the noise that was coming down his circuit, he couldnít have seen
it. So I now believe that probably we were the very first to see it because of Johnís excellent junctions.
The main thing I did, well the first thing I did in this letter was to, we were concerned about whether it was tunnel
current or current in micro shorts. Of course, very soon we came to realize that they both were basically the Josephson
Effect. Both were basically weak superconductivity, but in order to measure the Josephson Effect to make sure that we didnít
have to renormalize all of the quantities with a straight forward effect, we wanted to make sure it was tunnel current and so
I devised all of the checks that it was really tunnel current. That was what I contributed as an experimentalist to that
Then I had a dilemma. I was perfectly aware that Josephson had really discovered almost everything about the effect.
The only thing that I discovered, in fact, is what is now called the Josephson Plasma Frequency. I calculated the Josephson
Plasma Frequency, which is the natural frequency of oscillation of the Josephson Junction, the collection mode of the phase.
I calculated this, which was not in any of Josephsonís papers. It is now called the Josephson Plasma Frequency. So the only
thing about the effect that I actually really independently discovered is named after Josephson.
But nonetheless, we saw the very first Josephson Effect and itís in the paper. My dilemma was that I was aware of the
Matthew Effect, not the Peter Principle, but the Matthew Effect: ďTo him that hath shall be given. From him that hath not
shall be taken away even that which he has,Ē and I was deathly afraid that this would happen to Josephson and that I would
receive all of the credit for the Josephson Effect. Josephson wasnít that odd. I shouldnít have worried. Josephson was
perfectly capable in this kind of regard of taking care of himself, but I didnít realize that. He also had a lot of
advocates on his side, Pippard and Amuan [?]. But nonetheless, I was very afraid that if I published a real review article
in a prominent place about our observations that they would overwhelm his original discovery and I might get more than my
share of the credit. So I published it. I was very happy to be invited to this wonderful meeting in Ravello in southern
Italy on the Amalfi Coast actually, and to give a series of lectures on the Josephson Effect at this meeting, which was
published, and thatís why the main paper is this lectures on the many body problem, edited by Caianello, because I didnít
want to publish Josephsonís scholarship thesis essentially before he did, and he was very firm in feeling that he had
published all that and he didnít want to publish it again. So neither of us published the proper review in the proper place
until quite a bit later. That paper has some things in it that Josephson didnít think of. Josephson did later write a
review article that had some things that I didnít think of, so both articles are useful. Then the real review article that I
finally wrote was for Gorterís progress in low temperature physics. Thatís the complete story of the Josephson Effect.
Anyhow, it was from the Josephson Effect that I became aware of the Josephson Relation, and I immediately realized that
there was a possibility that superconductivity was not forever, that there could be voltages across superconductors because
the phase could creep by the motion of vortices. And at first I talked around to various people about how cosmic rays could
enter nuclei vortices in superconducting rings and so on and so on.
Itís interesting, it sort of prefigures the Betaloska stuff.
Yes, prefigures Betaloska and the various other ideas. And there was in fact some measurement of very slow
decrease of superconducting currents in rings that I think are a cosmic ray effect. I think such things exist, but it was
But then the second thing that happened when I was back home at Bell Labs was Young Kim came and visited me. He was in
one of the device groups. I forget who his boss was, but nonetheless he had been working on measurements of the critical
state which had been begun at the GE Laboratories. The work is well known, Beanís work, heíd been reproducing Beanís work
and thinking about it. He had a new geometry program for doing Bean type experiments, which were experiments on the residual
magnetism of a superconducting sample. He had a cylinder and he would put a magnetic field through it and measured the
magnetization; turn off the field and reverse it and watch the magnetization reverse, and so on. He said there is something
weird about this. When he would turn off the field, the current doesnít survive. The theory of the critical state says that
it should survive until I reach the critical field, and then it should die, and you could predict all the critical fields
from the Abrikosov Theory. He said but it should be superconducting, it is superconducting, but then the magnetization seems
to decay very slowly along this strange curve, he showed me the curve and I said, ďThatís a logarithm.Ē I didnít know why I
knew it was a logarithm, but in the two or three occasions in my life I spotted logarithmic dependences and all of them have
been interesting and have contained interesting physics. So I said, ďYour flux is decaying logarithmically. And the reason
it is decaying logarithmically is because the vortices are creeping through the material. The vortices are moving.Ē
And this I think was the first point in which people had realized that vortices are not forever; vortices creep. Even
Abrikosov never mentioned the possibility that his vortices could move through the superconductor. So there is this
Josephson relationship which says as the vortices move and reduce the magnetic field, then they will produce the equivalent
voltage across the superconductor, which will look like a resistivity. I looked up the theory of dislocation creep in solids
and I made the corresponding theory, and fiddled in various reasonable ways with that theory to make it fit the observations
and publish that as the theory of flux creep. Which I think is a new discovery in the sense of two things. One is the
connection between defect motion and dissipation generalizing that from dislocation motion, where it had been around for a
very long time, to the general idea that dissipation in broken symmetry systems is associated with motion of defects. And so
I believe that that is where that idea entered physics.
Later on, Kim caught onto the idea very quickly, and very soon he modified his samples in such a way that he could see
his flux. It not only modified his samples but increased the magnetic fields that he was using, and managed to get it into
the situation where the flux was flowing rather than just creeping. The flux lines were essentially doing fluid flow rather
than activated creep. In some of our later papers, the Anderson-Kim paper quite a bit later one, in ***Reviews of Modern
Physics Ď64 was the one where we jointly published those ideas.
Did you consider at all the possibility of going in the opposite direction and looking for localization of
vortices at that point?
Well, we realized that this was the reason why the superconductors were hard was they were full of pinning
[?] impurities, and thatís what Kim did was to remove the impurities, and then he could make the vortices flow instead of
creeping. Of course there was a lot of stuff that followed on from that. There was the work at the deGennes group about the
vortices being pinned at the surface, and surface conductivity and Hc3 as well as Hc2 and all that. But we didnít play with
that very much. So all of that followed from thoroughly understanding Josephson and how it worked.
A subsequent topic connected with superconductivity, weíre going to turn to the issue of phonon spectra and
tunneling, and perhaps you could tell us how this developed in your relationship with Bill McMillan on this whole subject.
It started with Morel, of course. This was the second of his thesis topics. He of course was doing it.
Where did Morel come from? Morel had been Pinesí graduate student, but Pines didnít get tenure in the Physics Department at
Princeton and he left in a huff and went to the University of Illinois, and he left behind his student Pierre Morel who
couldnít leave New York with him because Pierre was simultaneously the cultural attachť in the French Consulate in New York.
He was Nozieresí closest friend, but had competed with him for the affections of a certain girl who eventually married
Pierre. She was a very beautiful girl, and we knew them. And Pierre and his beautiful wife lived on a scale to which we
could only hope to become accustomed. But he came around and he was my student.
At the same time that I had been thinking about angular momentum states Iíd been thinking. Well,Iíd had to give a set
of lectures at Stanford about superconductivity, and over the course of those lectures I thought rather hard about the
interactions that went into superconductivity, and I realized that for the BCS model, the cutoff at the Debye frequency in
the electrons were in the interaction, and that K space was not the correct way of thinking about the interaction; the
interaction actually was quite spread out in K space, quite local, but that it was very long range in frequency space because
the ions are very slow moving. So essentially the kind of effect that took place was the electron went whizzing through the
unit cell, which started the phonons moving, and the second electron would go whizzing through that cell quite a bit later,
something like the phonon frequency later, and feel the effect.
So the seriously interesting problem was a retarded interaction rather than a long range interaction, and I started
thinking about how to express this retarded nature of the interaction correctly, and I set this problem for Pierre. Pierre
and I worked away at it for quite a while. I donít remember exactly when his paper came out; itís here somewhere. This also
is a Morel-Anderson paper.
Utrecht also happened in the middle of this problem, and there was a very, very dull, rainy expedition to the Polders
in the artificial lands in Holland, which we all got on the bus, and Bob Schrieffer and I sat down on the bus together, and
we whiled away this extraordinarily dull excursion by talking about physics, and I told him about my phonon interaction, and
he said the Russians had done something like that. I didnít even remember the Russianís name. Later on when Pierre went and
gave a seminar at Illinois, he dug out the Russianís name and explained the Eliashberg equations to Pierre, and so Pierre
reformulated what we had already been doing, in somewhat more naÔve terms, in the formal structure of the Eliashberg
equations. And then we had a fairly satisfactory kind of general theory of phonon interactions and how to deal with them.
There was no hint that I am going to do it a little better than that, but we certainly made various observations about the
structure, and we also made a table that kind of predicted, using the crudest possible model, the Jellium Model for metals
and Debye frequencies from tables and so on, made the crudest possible estimates of the transition temperatures and the
isotope effects. We observed that the isotope effect would be modified by what later came to be known as dynamic screening,
and even invented a neat way called the mu-star, an effective potential for taking in account the modification of the isotope
effect. Thatís what is left from this paper in modern theory, but in fact it was where the Eliashberg equations were applied
to realistic phonon systems. And we published it slightly before I went to Cambridge.
Ď62, Iíve got.
It was published in Ď62 but done in Ď61. I talked about this actually in Birmingham with Rudolph Peierls
in the audience, and Rudolph Peierls said, ďGee, thatís interesting. Isnít there some way that one might observe the
fluctuations in the order parameter that youíre predicting,Ē because among other things it predicted that the order parameter
would be a function of energy. In the conventional theory the order perimeter is a function of momentum, but in this theory
it is a function of energy and not a function of momentum particularly. In fact explicitly we have seen that it is not a
function of momentum. Eliashberg is often given a lot of credit, but in fact I donít believe he actually made any effort
whatsoever to apply his equations to real systems. That is strictly a formal structure. And our contribution was to make
the crucial observation that for practical purposes one could take the phonon interaction as local in space and long range in
time. So I said, ďWell, Prof. Peierls, youíre absolutely right, there should be some way to measure this.Ē Two weeks later
I received a phone call from John Rowell who had already started doing his tunneling work in which he said weíre seeing bumps
on the tunneling spectra of superconductors, of tunneling between superconductors. And he published a paper. Jim Phillips,
as his custom, jumped in on the theoretical side of that paper and said, ďHey, the two bumps there, look, youíve got
harmonics of the phonon spectrum.Ē Thereís one at one, and one at two, and he invented one at three. But at far as I know,
Phillipsí both reasoning and theory were completely wrong because what they were seeing was the longitudinal and transverse
peaks in the superconducting spectrum of lead. And so I said to, it wasnít Morel but probably Chynoweth who talked to me,
and I said, ďBut weíve actually calculated that kind of thing in this paper with Morel,Ē and suggested they look at Morel and
Anderson. When I got back, did a lot of talking with John Rowell, and one of the things I said was letís look at that
spectrum and see if we can calculate it with some reasonable structure for the phonon structure of the lead.
One other thing I had discovered or had received when I was in Cambridge was a print from Bob Schrieffer where he was
making the very first effort to take this Morel-Anderson-Eliashberg theory and put it online in an interactive computer mode.
So he was way ahead of his time in actually being directly online with his computer. So I was aware of that, and John
Rowell had produced very good bumps, very good tunneling characteristics, and we had discovered that the infrared spectrum
had these longitudinal and transverse branches, and so I invented a heuristic spectrum of infrared phonons, and took it to
Bob, and John and I went down and spoke to Bob. Bob had his students John Wilkins and Scott Scalapino with him, and they
said fine, weíll put that on our computer, and so we published Parallel Letters, Rowell and I with the experimental data, and
then with the computation using the Eliashbergís equations, and this proposed spectrum for the infrared phonons. That was
when, as far as I was concerned, and I remarked in a talk that I gave much later in Ď97, that was when the fat lady sang.
That was when you really knew that you had the ability to explicitly calculate the superconducting transition temperature
from the phonon spectrum.
That was when you really knew that you had the ability to explicitly calculate the superconducting
transition temperature from the phonon spectrum. I did a little more of that with Doug Scalapino because we got such
beautiful spectra that eventually the spectra became so detailed that I passed the whole problem onto Bill McMillan, who had
just come into the department as a post-doc, and Bill being a very stubborn and very brilliant guy, said, ďWe donít need to
postulate spectra and calculate the characteristics. Letís take the characteristic and calculate the spectrum.Ē And they
said, ďBut that involves inverting this very, very messy, integro-differential equation.Ē And he said, ďI can do that.Ē I
had heard at the same time about the fast Fourier transform technique that had been invented by John Tukey and suggested that
he use fast fluorae transforms, and he looked at me and said, ďI donít need that. Iíll do it my way.Ē And this was very
characteristic of Bill McMillan he did things his way. He said it very slowly, ďIíll do it my way,Ē [stuttering], but you
couldnít change his mind. But it was ten years later, he said, ďIt really would have been easier your way.Ē I felt very
vindicated, but he did it perfectly well his way. So he took the spectrum of John Rowell and inverted it and got the
infrared phonon spectrum, which by this time could be measured by an elastic scattering of neutrons. He got it bang on, and
the fat lady sang even louder at that point. So that was that. I didnít need really to interfere anymore in that problem
because once McMillan had hold of a problem, the competition was always left in the dust. So that was that.
Well now we have an important decision to make.
Shall I get started on localized states?
Maybe we could start on localized states. Now we have to turn back in time then and I suppose go back to the
end of the 50s and the early 60s and the development ultimately of your resonant level model for the formation of localized
moments. And what Iíd really like to ask you here is; what was your picture of magnetism at the time you went on your first
trip to England and participated in this meeting at Brasenose College at Oxford?
Well thatís where it came from, actually, because prior to that there was a famous bet. It may have taken
place at that meeting or prior to it. Walter Marshall and I, I forget exactly what was said then. John Ziman and Walter
Marshall both had the same complaint about me, namely that I had published their theses slightly before each of them. One of
them was spin waves and the other was, I forget exactly which. But anyhow, then Walter was by this time the supervisor at
Harwell and his group was doing, it was doing Mossbauer Effect on magnetic materials, and they were able therefore to get the
hyperfine coupling, the effective magnetic field at the iron nucleus in iron. But of course there was no way immediately to
deduce the sign, and I was fresh from doing the theory of super exchange, so I had a guess at this on how it would be the
super exchange effect that polarized the inner cell electrons, and that therefore the sign would be negative and Walter bet
me a pound that it would be positive, and indeed he paid that with signing a pound note. Unfortunately I lost it. This I
guess occurred at my visit to Harwell at the early Ď59 Cambridge meeting and they also visited Harwell.
May I just ask, how did you resolve the bet with the sign?
I donít remember. It was eventually possible to experimentally discover the sign. I think it was a matter
of, I donít remember. But itís a considerably subtler effect to discover the sign.
It was through the Mossbauer measurement?
Yes. I donít know, it may have been nuclear quadruple resonance or something, free resonance. Anyhow, at
this point we had just been freed at the Bell Laboratories. We no longer had to take permission to go to an international
meeting up the line of command all the way to the vice president and receive special permission to travel first class and all
that. You could damn well go when you liked it your departmental budget could stick it, and I was actually on a little panel
doing something or other for the National Academy. This panel was studying physics, sort of solid state physics or
something. So I could even get military transport. So I was invited to Europe again for the third time in a year and I
decided I would go. Brasenose College was having this discussion meeting of the magnetic transition metals, and I guess I
was invited because of Walter and our bet. Jacque Friedel was there and Andre Blandin and we talked about the in resonant
model of magnetic states in metals. I talked about this kind of super exchange idea, my famous parameter U that I had used
in the super exchange theory and how that might be relevant to the magnetic transition metals. But I listened very carefully
Then the other thing was we were a very close group of friends by that time, all about the same age: Ted Geballe, Peter
Wolff, but particularly Bernd Matthias. That was quite a social group that focused to some extent around Bernd Matthias.
Harry Suhl worked with Matthias and Matthias and Clogston were in the process of studying the effect of magnetic impurities
on superconductivity. This in fact was what I talked about at that meeting in Toronto where I bad-mouthed the Abrikosov-
Goríkov theory of magnetic impurities and superconductivity, and Iíve always regretted that because I was quite wrong; their
theory was right and Harry Suhlís theory was wrong. I think they forgave me for it, but I never forgave myself.
Anyhow, these experiments would take a superconductor like lead, or I think they used aluminum very often, I donít
remember what they used, but they would put various magnetic impurities in it and measure how much effect that had on the
superconductivity. But Bernd said, ďLook, if I put iron in such and such a compound, if I mix iron and rhodium, or a
compound or iron and rhodium, this compound isnít bothered at all. The iron electrons join the D band and become
superconducting.Ē So there was this very sharp dichotomy between these two possibilities. You can have samples in which
iron was a component of the superconducting compound, or samples in which iron, as in molybdenum, iron would completely
destroy the superconductivity. Bernd only discovered that molybdenum was super-conducting after he reduced the trace amount
of iron to 10-6 in concentration. So we were very conscious of the great sensitivity of superconductivity to magnetic
I realized there is this crazy dichotomy between cases in which the magnetic impurity was magnetic and cases where it
wasnít. And as in many examples that have occurred in my life, I realized that I was bothered by this dichotomy and that it
was an open-and-shut case. It wasnít some delicate experimental fact like the Knight shift, or like the Lamb shift, that you
had to go to extreme effort to discover. This was, this really stuck out like a sore thumb, this dichotomy. So I said,
ďThere has to be a theory for a dichotomy. Itís simple enough, simple as that.Ē So I started from this idea that Iíd
borrowed from Blandin and Friedel at the Brasenose College discussion, and my parameter U, which they hadnít had, and I said,
ďLetís do a resonant state with the parameter U on the local state, and thatís the localized magnetic model,Ē the point being
to show that if you had one value of the relative strength of this parameter U versus the breadth of the resonance, you would
have a magnetic case. If you had another value, it would turn out not to be magnetic at all. I didnít really discuss at the
moment whether this was a sharp thermodynamic transition; I just said there are these two possible electronic cases.
I guess the only footnote I would make to that is that it was four or five years before I realized that there was a
serious problem with this, that the problem was there couldnít be a phase transition. I even talked about it informally in a
talk at one of the ubiquitous magnetism meetings that we had. The next year Bob Schrieffer talked about it. He was
beginning to think about Hubbard-Strotonavic (?) and that kind of structure. I think I was quite wrong to be a little
annoyed that he didnít mention that I had talked about it at actually the identical, same meeting a year before, that there
might not be a sharp transition and that there would be fluctuations. But in fact, I think there was no reason why he should
have. I was wrong to be annoyed. So it should be remarked that Bob was the first to get in print with the idea that this is
not a sharp phase transition, but that there would be fluctuations and eventually you had to worry about whether the
magnetism remained or not. So Bob, essentially he didnít solve it, but he did initiate the theory in a formal way, the
theory of renormalization of the Anderson Model.
So we are here today for a continuation of our discussion series with Phil Anderson, and we will take off
today where we left of the last time on a discussion of his work on magnetic moments in magnetism, and I will turn the mike
over to Pierce Coleman.
Phil, I wanted to ask you to begin our discussion about local moments, the Anderson Model, and the Kondo
problem, about when you first became aware that the fact that the sign of the interaction between local moments and the
conduction electrons was actually anti-ferromagnetic.
Well that actually dates back to 1959, which was the year I decided to make up for all of the time I had
not had the privileges of my academic colleagues in traveling to Europe. So I went to Europe three times during the course
of less than twelve months in 1958. I told you about the trip to Moscow and I think I told you about the trip to the
superconducting meeting in Ď59 and in June Ď59 when Joyce and Susan came along and we traveled all over England as well as
visiting Harwell and Cambridge. There was a third trip to a little meeting at Brasenose College which was organized I think
by Kurti and which was where, I guess I have told you, that I learned about Blandin and Friedelís virtual state idea for
impurities in metals, and I gave a talk there. Here it is, ďDiscussion Brasenose College, Oxford, England: New Concepts in
the Magnetic Transition Metals.Ē There I made the statement that the sign of the coupling between the conduction electrons
or the magnetic electrons and the rest of the conduction electrons also in their shells would be negative, and that I think
may be where I made the famous one pound bet with Walter Marshall that he would find the opposite sign for his hyperfine
interaction in cobalt.
That led eventually to these two very obscure publications with Al Clogston: ďAnti-ferromagnetic Contribution to the
Polarization of Free Electrons by Inner Shell Spins.Ē They are just two abstracts in the bulletin of the APS, and the
argument is two things that are involved there are what I call the Compensation Theorem, that there would be a ferromagnetic
and anti-ferromagnetic contribution to the polarization of the free electrons which would more or less cancel at any point
far from the impurity. I said there is an anti-ferromagnetic contribution to the polarization of free electrons by inner
shell spins, so thereís the sign right there in the Bulletin. That also, incidentally, is the physics behind the
localization of the Kondo resonance, which ever since then has always puzzled experimentalists because theorists go around
talking about a Kondo cloud as though it really existed, but in fact there is no long range spatial structure in the Kondo
effect or in any of these anti-ferromagnetic polarization effects. I didnít really understand exactly why, but I got the
right answer in this compensation theorem, that if you insisted upon thinking of it as separate ferromagnetic and anti-
ferromagnetic contributions that these two cancelled. And thatís the long range part. So there is no long range
polarization, except that there is the Friedel oscillating polarization, which was observed actually by Charlie Slichter in
the NMR. But there is no long range and that question came up about two weeks ago when we were looking at the STM studies of
the Kondo resonances, and they find, indeed, thatís itís totally localized and itís the same story as this little bulletin of
the APS paper.
Then we went on and talked a little bit more in detail about that, and this thing that you were pointing out to me in
Ď64, ďLocalized Magnetic States in Metals.Ē There was a Nottingham Conference. That was the International Magnetism
Conference, which was held in Nottingham that year, and since I always like to go to England if possible, I went to
Nottingham and gave a talk about these various questions. The basic question I was studying there was does the Schrieffer-
Wolff Model have the same effects as the Anderson Model? Are the both localized and are they both confined to a single
space? And there I think I made the first comments about the Friedel Sum Rule and so on. I calculated phase shifts.
Now at that stage, I think the Schrieffer-Wolff transformation must have been published in Ď65, if Iím not
Was it really that late?
If Iím not mistaken, but maybe the work had been done before then.
Well I think Wolff had it in his notebooks much earlier. He produced it essentially at the same time that
I talked about the localized state. He came up within the next few weeks.
Already in Ď61 or so?
Already in Ď61, essentially as a response to my paper. He said, ďBut you can also do it with the states
from the band itself,Ē a localized U rather than a localized orbital.
So by the time youíd reached Ď64, the equivalence between the [???]
Thatís why itís the Schrieffer-Wolff transformation. He had done it, and then I guess Schrieffer gave a
talk, there were two magnetism meetings and I talked at one and Bob at the other. I talked last time about Bob having said
there were problems with the Anderson Model. But he gave his talk in connection with announcing the Schrieffer-Wolff Model
because Wolff had done it all in Ď61 and I had referred to it in various talks since then including this one. But Bob did of
course a much neater job, and he began the process of studying the dynamics of the problem at low temperatures. See, I was
still in this paper talking about basically a resonance, and I began to notice the Friedel Theorems. In the first place, the
total number of electrons in a resonance; and in the second place, the fact that the electrons were certainly confined inside
the interaction region, the only region where there was any difference from essentially the free electron, scattered wave
functions, so that the phase shift at a given radius told you how many extra electrons there were inside that radius. So any
extra electrons had to be inside the radius, beyond the radius of the interaction region, inside where the basic wave
functions were modified.
Now in your Ď61 paper you used a mean field theory to describe the development of the local moment, a very
frozen picture of the local moment. Can you tell us a bit about the evolution of that picture from something looking rather
like a phase transition into a picture where it became apparent that the moment quenched as a slow cross-over. How did that
Well, I think the first hint was really Bobís talk about the Schrieffer-Wolff Model, and he said something
that amounted to, he thought the problem of low temperatures was a serious one. The littler of lines of thinking in this
1965 paper at the Nottingham Conference, I was still thinking Hartree-Fock and thinking in terms of phase shifts, but I had
understood that essentially the exchange interaction was the phase shift compensating for the business of, for the assumption
of a spin a half, so youíre essentially transforming from Anderson to Kondo and by treating it as split resonance and doing
what we now we call a JT transformation, replacing the U by infinity and then compensating it with an exchange integral.
Thatís talked about at least in this paper.
There was the other thing that was going on was the work on the Kondo problem. Well, there were several things going
on. There was the work on the Kondo problem. I didnít work on it, but I did publish it because both of the two first
sophisticated papers on the Kondo problem were published in my journal, Physics. There was an Abrikosov paper and a Suhl
paper. Suhl was trying to do it with dispersion theory, kind of I would say rather ad hoc generalization of dispersion
theory that sounded very fancy mathematically, but it wasnít any better than any of the other approximate methods that were
being used. And Abrikosov of course had his slave-fermion model that was also published in my journal. So the two basic
papers were published in this journal weíre going to be talking about later.
Maybe one thing we would be natural to move towards is your paper on the infrared catastrophe, which was
published in 1967. Because clearly by the time youíd gotten to that, youíd begun to be aware of infrared effects in these.
Yes, we began to be aware of the Kondo effect in the logarithmic divergences, and we did these localized
magnetic states and Fermi surface anomalies in tunneling which was essentially saying a localized center, a magnetic atom or
something in the tunneling barrier was going to act like an Anderson Model, and that was going to have a Kondo effect, so we
calculated out the Kondo effect. This was me and Joel Appelbaum, who was post-doc at Bell at the time. So we realized, I
mean that was the only paper I did in this particular period on the Kondo effect. But I was obviously beginning to realize
that the Kondo effect was going to happen for the Anderson Model or the Londo (?) Model. It just didnít make any difference
which representation you wanted to use. You still had the mystery of the Kondo effect. And the Kondo effect was clearly the
low temperature behavior of the Anderson Model, and by this time everyone was really worried about it.
So by Ď66 the experts had become aware of that?
Yes, the experts had become aware of that. People were trying, well, Bob and I think John Hertz was trying
to do the Anderson Model with path integrals. Don Hamann worked on it around that time. I donít really know why they didnít
quite get the answer right, but they never did and they used Hubbard Stratonovich and it didnít seem to come out right and
the answers were ambiguous and Iím not sure what their mistakes were. One mistake that other people made later on, and it
may have been the same mistake in their problem, the Luther Emery group had problems that they were using essentially a spin
rotation invariant forumulism, but they werenít using spin rotation invariance boundary conditions. They werenít using
cutoffs that were spin rotation invariant, and so they got into a totally terribly wrong answer because they lost spin
rotation invariants on their cutoffs. I think that would have been an equally easy mistake to make in the Hubbard
This is a bosonization approach to the problem?
Well, no, but in the Luther Emery it was a bosonization approach, but you could do the same thing with what
the other guys were doing.
Well, I guess the next thing chronologically was the paper at the Varenna School, this big paper with Bill McMillan.
And there is something thatís wrong about that and something thatís right about it. What is right about it is I re-derived
Friedel from a really rigorous point of view. Until that time I think most people had thought about the Friedel Theorems as
having to do with moving the electrons in and out through the boundary, and that always leaves you open to the question of
are you treating your boundary conditions right because youíre essentially using Sturm-Liouville theory and boundary
conditions, and I tried to find a boundary condition invariant independent way of doing it which involved simply integrating,
taking the local Greenís functions using outgoing boundary conditions which were completely independent of what happened at
infinity, and I found a way to derive Fermiís or Friedelís work that way, which I think he has in some obscure paper because
some of the Frenchmen in the audience said Friedel did all of this, but he didnít publish it or it isnít published openly.
Then I had this paper, this attempt to do random alloys of transition metals, which was a very ingenious, beautiful
scheme and we did a lot of computer work on it, but in the middle of the computer programming, since I wasnít very good at
programming I left it to Bill McMillan and he made a mistake. He replaced tan theta with 10 theta(with one little line in
the program theta Ď 10 theta. So everything in the paper had 10 theta, the scattering non-periodic in theta, and it made the
resonances too broad instead of too narrow and they didnít resemble at all what we were looking for. So the impurity part of
that paper, the random impurity scattering problem was wrong. See that Bill had just been working on the Effective Medium
Theory. I forget what else itís called.
CPA. Bill, the young post-doc, are co-inventors of that with the guy at Penn who is normally credited with
But he kept the N and N + 2 states on one side and the N and N + 2 states on the other, so he realized that
he could somehow measure the phase. He did this because he wasnít sure. I think he had done it at first the right way, but
he wasnít sure that people would accept it. Anyhow, I read through this thing and he had four separate terms and I only read
one of the terms and I said, ďI canít see anything wrong with it,Ē and from that point on we discussed this and he came to
the T Table Summit more often and we discussed it and at length. We didnít really understand totally what the interpretation
would be. Now Brian Pippard claims that I was the first one who said, ďOh, I suppose itís really a current proportional to
sine phi.Ē The expression that Josephson had didnít make that explicitly clear. So according to Pippard, that as part of my
role and part of my role was just to say, ďWell I was really persuadedĒ talking to the convinced I guess in Josephsonís case,
but I certainly persuaded Pippard that it was all right, that there was a phase and that this was a thing that one could
calculate, one could expect due under physical results.
Aside from that I didnít have much of a role in what Josephson did, except to say, ďYes, itís real. Itís fine. And
itís important that it is actually an explicit way of measuring the phase of the order parameter, the important constituent
in the order parameter.Ē He was responsible, for instance, for finding the tiny little bit of Goríkovís derivation of Landau
Ginzburg that said that the phase varies with the either the exp (i mu t0, in other words, the Josephson relation for the
frequency, which Josephson cribbed out of Goríkov, but it had no prominence in Goríkov at all. So he realized that it was
going to have this frequency dependence, entirely independently. He realized how one could measure the frequency dependence
with the driven nonlinear effect. And he had the right dependence on the penetration depth. I later re-derived that and got
the wrong answer and sent it to him, and he wrote back and said, ďYou have the wrong thickness in your dependence on magnetic
field,Ē and sure enough he was right.
So I was enamored of the CPA because people had been fooling around with diagrams, and Klauder had been
fooling around with diagram summations for random lattices and Lax had been fooling around with them, and they seemed to get
nonsensical results and the CPA kind of summed these things in what seemed to be a much cleaner, straightforward way. Itís
an effective medium theory or CPA or whatever you want to call it. But itís very nice and I tried to use this for transition
metals, and it would have been just find except for this horrible mistake in the middle, which a student named Olsen of
Walter Kohn took as his thesis topic. Walter told him, ďHeavens, you mustnít publish this. You are saying that Phil
Anderson is wrong.Ē So he never even sent it to me. Then when he finally sent it to me, I immediately published an erratum
and wrote an apology to him, an apology for Walterís behavior to him because he was absolutely right. He was absolutely
right all along.
That was not the formal theory of resonances, but I havenít yet gotten involved in this infrared catastrophe. That
followed from Gerry Mahan coming to Bell and giving talks about his work on x-ray edge anomalies. He was calculating the x-
ray emission problem and x-ray scattering problem in metals, and he got involved rather deeply with doing the perturbation
theory correctly, and so when he came to actually calculating the basic process, which is the Greenís function for the
electron, he only did two orders of perturbation theory, but he noticed that the second order of perturbation theory was
diverging worse than the first. And so he said, ďI think thereís a logarithmic divergence here.Ē And again Walter Kohn is
the villain you know, heís such a nice man, everyone thinks heís wonderful, but heís the villain of this. He had written a
paper with Majumdar, which was already in the literature and weíd all read it and thought it was very brilliant and
wonderful, and he showed firmly that when you create a bound state in the Fermi liquid, it had no particular effect in
causing the singularity of the Fermi surface. He was creating the bound state adiabatically, and so in three dimensions you
would have no bound state, just a resonance, and then thereíd be a critical potential where it would bind. And yes there was
a singularity at the bottom of the band, but if you looked at G(k) for kís near the Fermi surface, there was no singularity
whatsoever at that point. Which is right. Of course thereís no singularity whatsoever.
[???] in the occupation.
The occupation n(k) or any other. He calculated n(k) and he even said, ďWell, itís probably true even for
interacting electrons in Fermi liquid theory.Ē And Jerry was getting this singularity at the Fermi surface when you turned
on a potential. But of course the problem was that Walter was turning on this potential continuously and Jerry was
discussing the question of turning on your potentials suddenly and comparing the ground state without a potential to the
ground state with. But he didnít understand that thatís what he was doing because he had so much perturbation theory and
before he ever got to the question of calculating the Greenís function that he thought of the Greenís function as something
he was going to have to calculate one term at a time. And somehow he only got two orders of perturbation theory and didnít
realize there was a general theorem here. He did extrapolate. He did say, ďThis is probably logarithmic,Ē and he had more
or less the idea where the logarithm came from. So itís really a little unfair that I got the results of this Phys Rev
Letter. But I then actually saw what had to be done which was to compare the ground state of the system with the potential
to that without the potential, and I saw that there would be a divergence even in second order perturbation theory in the
potential. So this was simply the statement of that divergence.
John Hopfield tells me that he more or less understood that. John one time when he was visiting Cambridge said, ďYou
know, all of this Kondo problem and the impurity problem, I was sitting holding the hand of whoever was making these
discoveries, but somehow I never got my name on any of the discoveries,Ē and he thought it was a little unfair. And I said,
ďOf course itís unfair and I wish Iíd put your name on it,Ē but by that time all the papers were published. But then youíll
find in the eventual work on the Kondo problem youíll find effusive acknowledgements of Johnís help.
But anyhow, we had the Fermi infrared catastrophe, and I realized fairly soon that something that you could apply to
the Kondo problem, that there was an infrared catastrophe appearing in the Kondo problem when you flipped the spin, you would
get infrared catastrophes for both spins. And I tried like mad to work out what would really happen, and there are two
papers here which are unsuccessful attempts at that, the Phys Rev 1967 and Localized Moments at the Les Houches summer
In the course of doing that, letís see, what had happened? The first thing that happened was I was really stupid. I
could get the infrared catastrophe at T Ď 0, and I didnít even think about thinking that if I had the infrared catastrophe
more or less in real space I should equally well have the infrared catastrophe in frequency space. So at this time I was
totally unaware that I could also get the energy dependence of the infrared catastrophe, I could not explain using this
method alone, couldnít explain the actual x-ray edge singularities. And that had to wait for these enormously long heavy
breathing papers by Nozieres. Nozieres and Gavoret wrote three terribly long, terribly difficult papers. He finished three
papers and then he gave the talk at the Ecole Normale and deDominicis was in the audience and deDominicis raised his hand and
said, ďBut you can do it on the back of an envelope,Ē and showed him how. That was the result of that, the fourth paper,
Nozieres-deDominicis. And Nozieres was really trying to do it by old fashioned Fermi liquid scattering theory and it took
three heavy papers, and if you thought that maybe one of your propagators would not be analytic in omega but could possibly
be a power law and then really calculated the propagator correctly, that was the propagator for the localized mode, that was
deDominicisí idea, and you immediately get the power law propagator. And Yuval was already my student and explained this to
him he said, ďYou idiot, of course this is true.Ē (I mean, that was the way that he talked to his supervisor.) If you just
realized that the electrons have a linear dispersion curve, that they have a constant velocity, then the orthogonality for
whatever range the electrons have reached to at a given time gives you the time dependence of the orthogonality, so you can
substitute distance for time or substitute sample volume for time there, they are interchangeable so you get the same power
of the time that you get of the volume. So this paper immediately became an even simpler way of doing Nozieres-deDominicis.
Somewhere in, I think itís in the ground state paper, I had spent a long time thinking about how to actually calculate
for finite phase shift because, of course the phase shifts for the Kondo problem were large. I arrived at this method using
the Cauchy determinants for the orthogonality, which is essentially taking an asymptotically correct wave function, a free
electron wave formation with a given phase shift, and realizing that the overlap is essentially the sine(delta)+ deltak. Or
no, one over sine? Anyhow, it ends up that you have a Cauchy determinate of one over [???] plus phase shift and this Koshi
determinate, thanks to Luttinger, I learned how to evaluate, and it gives you the power law, the generalized power law with
the exact powers as Nozieres-deDominicisí had them. The power is the phase shift squared rather than the sine of the phase
shift squared. So then I had a way of deriving that, which is I think quite a bit better than Nozieres-deDominicisí. What
is an even better way is probably Bosonization. I donít know, but we hadnít yet thought about bosonization.
So that was in the Ď69 paper?
This is in the Localized Moments, this is on page nine. I give determinatal technique in the lectures.
And youíve already started working with Yuval by that stage.
Yes. Okay, letís go back. Life. Nottingham. Then that was the summer of Ď64. The years Ď65, Ď66 were
when Paul Richards was making this horrible blunder trying to find the Josephson effect in superfluid helium. The first
paper was Richards and Anderson and Iím still not convinced that we hadnít found the AC Josephson effect in that first paper.
We were using differences in levels, and we were essentially doing the AC Josephson effect in the driven technique. We were
using differences in liquid levels, and in the original paper we had open pipes. Paul decided it would be much better to do
it with closed pipes, thereby introducing acoustic resonances in the helium above the closed pipe, and he would then leave
the level of the helium at the same point so any acoustic resonance was maintained by having the pipes closed and not
allowing the helium to evaporate. And it was a much, much more accurate experiment, and it was a very accurate way of
measuring acoustic resonances in the system, but it was a mistake. I still donít know whether the level of pinning that we
saw in the original experiment was an AC Josephson effect or not. Nobody has ever repeated the experiment. Itís a very hard
experiment and very sloppy, and it certainly was imaginative to say there were resonances there.
But of course the Josephson effect has been recently...
It has been seen since then, but not in that kind of rig, which was very primitive. But you know, when the
level difference was that high, there were vortices going across the aperture at the appropriate rate and so they could have
been synchronized by the AC. And there couldnít have been resonances in the open tubes because they would have had to follow
the liquid levels down as the helium evaporated, so it was automatically protected against there being acoustic resonances.
Anyhow, I went and talked about the superfluid helium at Sussex, which, again, was my summer vacation. I would love to go to
England if I could, and I had a very pleasant stay in Sussex and then I walked on the South Downs before they became
overcrowded, and gave a talk about the flow of superfluid helium, which does have an interesting theorem in it. It shows
that the Josephson theorem has a certain amount of classical meaning. It shows that you can also calculate, in an
incompressible perfect fluid, you have the rate of vorticity motion equal to the chemical potential difference, even in the
Definitely you want to link this up with Yuval.
No, no, this is totally different. I decided weíd better go back and clean up all these things. Iím
trying to remember. Then the next summer I went to the Walter Marshall Varenna Summer School, and it was all about magnetism
and we were all thinking about resonances in transition metals. There was a very nice paper by Jim Phillips about resonances
in transition metals in that meeting. Youíll also find a good paper by Volker Heine. By now Iíd met Volker Heine and he was
a pretty good friend, and we were all talking about magnetism in terms of resonances, together. That winter I was sent by
University of Cambridge a first class ticket and traveled for about two days by first class ticket and signed my appointment
as permanent visiting professor to the University of Cambridge. I remember at the Varenna Summer School we had this table
full of people that were very friendly and close. There was Fred Mueller, you wonít believe that Fred Mueller got along well
with people, but that was while he still had his nice wife Kay. And Seb Doniach and Seth Silverstein and me and Jim Philips
also got along well with this group. It was a very congenial group. The only problem with the meeting was thunderstorms the
thunderstorms in the spring on Lake Como concentrate on the edge between the water and the land, and Larry Walker was
determined that he was going to get out of there as soon as possible. He thought that this was a danger over and above the
appropriate, that physics wasnít worth being in danger of your life every night. But otherwise the lake was wonderful and we
swam in it a lot. I remember Walter, who already looked rather like a blimp, he would take his two or three young children
and they would kind of float on his belly like a blimp. He later became Lord Marshall, of course, but he was not Lord
Marshall yet; he wasnít even Sir, I believe. But I had to keep quiet to all the Englishmen that I was signing a deal to go
to Cambridge. But then that winter it was properly announced and I met the Vice Chancellor and signed up.
Why did you have to be quiet?
Because it hadnít been formally announced yet. The electors had met and suppressed the chair and replaced
it with a visiting chair and all that, but it hadnít really been settled yet until I put my little hands in the big hands of
the Vice Chancellor and signed.
And presumably Neville Mott was the driving force.
Neville was the driving force. He had come to Bell I guess on his way to one of these magnetism meetings,
and heíd asked me who would be a good person to capture back to Cambridge with his new professorship. And of course the
sneaky, downy bird that he is he said, "Well, of course, you wouldnít want to go,Ē and I said, ďNo, absolutely not,Ē and
started suggesting names. "Under what conditions would you go?Ē he said. And I said, ďIf I could stay at Bell half time.Ē
I was tired of turning down offers from various places. Iíd turned down a suggestion, well, 1960 I turned down Stanford
which is the only one I ever really came close to regretting. But Iíd turned down various other places and Joyce said to me,
ďIf we are not going to take this one, weíll never do anything adventurous.Ē And so we decided it would be an adventure and
weíd do it and he made this arrangement.
And so I went off to Cambridge. But before I went off to Cambridge I had a three weeks Regents Professorship at La
Jolla which Bernd Maatthias had arranged for me. At La Jolla there was Christian Caroli whom Iíd met at the Ď63 meeting in
Ravello and become very fond of and both Caroli. Ravello was kind of the ultimate perfect meeting, everyone who was there
kind of classifies it as that. So it was nice that she was there and Bernd was there, Zachariasen was there, Maki was
spending a year visiting.
We talked a lot about the infrared catastrophe and that work with these various people. Oh, and Harry Suhl was there
and I talked a lot about the Kondo effect with Harry. And also I spent the time preparing the Regentís lecture, and that was
the occasion in the spring of 1967 when I gave the Regentís lecture. Joyce had flown to England because our real estate
agent said thereís an auction of a house and we think youíd like the house, and Joyce walked into the house, took one sniff
and realized that she was smelling dry rot and turned it down, but she found another house which we liked very much on Little
St. Maryís Lane. It was also practically rotting into nothing but it had such an incredibly good location that we decided we
wanted that and instructed our real estate agent to buy it. Then she came flying over from England, stopped off at our house
which had, in fact, been trashed by a close friend of Steven Holdenís who was working at the same private school where he
was, but what Steven hadnít know was that he was a druggie and had a druggie girlfriend who was a Polish immigrant and they
kept having fires in the fireplace, but they didnít know anything about dampers so they never opened the damper and all kind
of mess was made. So she helped clean it, and called Steven and Steven came over and worked very hard at helping her clean
it. Then she left for California on a night flight and the flight circled around Chicago and circled around Milwaukee and
was not supposed to come, and then I guess they were on the ground in Milwaukee and Bernd and I and Zachariasen were playing
Hearts, it was one of his all-night Hearts games drinking and finally Bernd called up the president of American Airlines and
said, ďYouíd better let that plane come. It was unconscionable.Ē I donít know why he knew the president of American
Airlines or why he had any influence on the president of American Airlines, but it worked. And so Joyce, at about four AM
flew into San Diego airport. This is the kind of thing Bernd did on a regular basis. Heís supposed to have been an
extraordinary character, and he was. Of course the reason he stayed up late at night playing Hearts was so that he could go
into his lab after the end of the Hearts game and make sure all of the students were working overnight. It sounds endearing,
but it wasnít necessarily. But we had a good time with Bernd and we would go to this Mexican joint with he and the Carolis
and sing. Christiane had a great store of French folk songs and we had various songs and we had a great time in this Mexican
joint. But thatís where ďMore is DifferentĒ came from, that was the Regent selectorship.
So then I went to England and we thought we had signed and sealed. Well, you know, in America real estate deals are
you shake on it and itís done. We didnít know about gazumping, but somebody gazumped us out of our house on Little St.
Maryís Lane and we ended up in the coldest flat owned by the University of Cambridge and thatís saying something, in a place
called South Acre. Typical English, a marvelous picture from outside and the most miserable accommodation you can possibly
imagine inside. Well anyhow, we lived there for the appropriate amount of time and had a brand new house, we bought a brand
new house in the course of being built and we were able to live in that the next year.
In the meantime they had found me a demonstrator, John Lekner, and set up and I was head of the department, or the
group anyhow. Josephson was a member of the group, John Lekner and Volker Heine and all his friends and relations, all his
post-docs and we got along like a house of fire, and Volker had reserved some of the smartest, he got the ragtag and bobtail
(he got Basques, he got Turks, he got Israelis, he had an Ibo among others, and I donít know if he was a Tamil or a Sinhalese
named Appapilai that we called Apple Pie, and he had this weird bunch of students.
Quite multicultural, indeed.
Well we were multi-cultural. Oh, and we had a Northern Irishman later, Dave Bullet was a Northern
Irishman. But miscellaneous students and some of them were good and some of them not so great. Wai-Chao Kok. There was
this guy and he ended up he was really no good, Keith Woods, ended up in the Road Research Laboratory. But I got Yuval and
he was good, although difficult, because he believed that his role in life was to have the ideas and my role in life was to
write them down, and I kind of saw things differently. But he stimulated me into going back and thinking about the infrared
catastrophe paper and all that, and we worked on the Kondo problem. And I guess the first paper we did was the exact results
in the Kondo problem, which was the equivalence to a classical one-dimensional Coulomb gas and that was with Yuval. He took
this result of mine that the infrared catastrophe had a phase shift in it and he found a way which he thought was much
better, which was the Muskhelishvili equation which was equivalent to bozonization, equivalent to any of the ways of
essentially doing the repeated interaction diagrams between two spin flips. So he had the idea or he showed me that the
infrared catastrophe problem was a Muskhelishvili equation. And I went home for the summer, summer Ď68, and thought very
hard about it and came back with the sum over spin flip paths, and I said, ďThis spin flip path with Muskhelishvili equation
tells us that this thing is really a classical gas of spin flips, and thatís what we have to solve.Ē So thatís the basic
It took us several months I think then to do the Phys Rev B1 paper which is equivalent to the second Phys Rev B1 paper,
the Anderson, Yuval, and Hamann. The reason the Anderson, Yuval, and Hamann paper appeared in Ď70 is that it was stopped by
the referees in Phys Rev(Phys Rev, not Phys Rev Letters, we werenít even trying to get something into Phys Rev Letters. The
referee, Bob Schrieffer had admitted, was him. He said he didnít believe it apparently and I gave the talk at a little
symposium we had in 1970 sometime in the summer and explained the methods in some length. This was the US/Russian symposium.
This was one of the periodic thaws that we had in US/Russian arrangements, so I think Goríkov and Dzialoshinskii had been
sprung. Goríkov and somebody else had been sprung from Russia, and they had this special symposium for this group of
Russians who had come out. I gave the talk, and Bob stood up and admitted how he was a referee and he was sorry and he was
going to instruct them to publish it.
But it was published in Ď69, and I didnít know about the renormalization group, I thought I was inventing it. The
first thing I realized was this method I called renormalization by leaps and bounds. I would take what was essentially the
blocking phase transition and would take all the — well, it was very like what Wilson did later. I was renormalizing
logarithmically taking bigger samples, bigger lengths of flipping sequences and taking them in a logarithmic sequence or an
exponentially increasing sequence, doubling it and then doubling it and then doubling it, and I called it renormalization by
leaps and bounds, so even that I had. But then I realized one could just do it within continuous renormalization and that
they were both exact.
And we kept track, we had to keep track very carefully of the spin rotation symmetry, because one component of J was
the fugacity for hops, the number of spin flips that you had, and the other component of J was the strength of the
interaction between spin flips, so itís not at all obvious that these two renormalize at the same rate. But if you were
careful to make sure that the cutoff was the same for both integrals, then you can all right do the renormalization on both
together, and you found that there was this simultaneous renormalization of the coupling and of the magnetization and of the
fugacity (all three renormalized not quite at the same rate, thereís a factor of two between each of these which were factors
of two that Wilson didnít find exactly, we found them exactly. So Iíve always contended that our method was better than
Wilsonís. It subsumed Wilsonís but it was better because it could achieve the Wilson factor. It was the Wilson ratio, as a
matter of fact, that we got as exactly two by this method.
And the existence of the first paper is that Gideon got very antsy about not getting his thesis published and so he
insisted on writing the Phys Rev B1 1522 paper which was premature, and then we published the full paper which was Anderson,
Yuval, and Hamann, or we got that in past the referee, past Schrieffer. So my priority on that was destroyed by Bob
Schrieffer, although itís not the full renormalization group and I was not paying any attention at the time to any of the
questions of universality and so on. But in fact, it is an equivalence to a classical statistical system, a classical one
dimensional Coulomb gas, which was at that time and unsolved statistical system, and we pointed out that we had also solved
the statistical system in J Phys C.
Thereís Ď70 and thereís Ď71. Both have this discussion. What page is that Ď71 in?
Ď71 is page 11 near the bottom.
Oh, yes, thatís it. Thatís the Kondo problem and the statistical model. I was insulted when Dyson
referred to these results as a conjecture but I suppose from his point of view and from a mathematiciansí point of view, itís
a conjecture. He was correct. He had done the whole one dimensional problem except that case.
I was just going to ask, his work came prior to this?
About the same time, but he refused to commit himself on the exactly two problem, he hadnít solved that.
He said it involved logarithms and he didnít know how to sum the logarithms. We did. So we did sum the logarithms.
What happened to Yuval actually?
Heís now working for Microsoft. Heís working for Jennifer Chayes. He spent a long time in Israeli
intelligence and then he came and worked for Microsoft. Worked directly for Nervald, the Princetonian whoís in Microsoft.
He was at Microsoft.
Yes. He was at Microsoft and then transferred into Jennifer Chayesí group. I donít know what he does for
them. Jennifer told me that he still expects her to write down the results that he finds. He hasnít changed a bit.
One last thing. Exactly how did Don Hamann get into that?
I think he was in charge of showing that it was okay for the Anderson model as well as for the Kondo model.
He showed that you could do certain path integrals in the real model and it would come out with this result. But I donít
remember exactly. It was fairly important, but it was not — What Gideon and I had done is already essentially there in that
Don was a post-doc at Bell at that point?
No, I think maybe heíd become an MTS.
Just to finish off our discussion of the Kondo problem, when did the picture of the Kondo facts leading
ultimately to a Fermi liquid ground state start to emerge?
Well, that was already in these papers with Yuval and Hamann, and particularly this inverse square one, the
Ising Model, because from all the fancy methods that people were using when the question of what did it exactly renormalize
to became very dicey. In fact Nozieres didnít give up at that time and I think has only recently admitted that, in fact, it
was obvious that it renormalized the way it does.
But to us it was absolutely obvious because we all along had this triple relationship, essentially, the dual
relationship between the Kondo problem and the inverse square Ising Model and also the relationship which is equivalent to
the Coulomb gas. So thereís a duality between the quantum problem and the classical statistical mechanical problem. The
quantum problem becomes hard where the classical statistical mechanical problem becomes obvious. Thereís no way that the
classical statistical mechanical problem is going to renormalize to anything but the free paramagnet, and that is basically
the Fermi liquid. Various other people liked the idea of stopping the renormalization at essentially one on the J-axis or
the axis on the famous K diagram because that could be shown to be equivalent to free particles, but there are things that I
donít really like about that because that doesnít necessarily get you all the right parameters. I would rather say it
obviously renormalizes to essentially no free moment because the spin flips become absolutely random.
So it was obvious to us what the answer there was, but we used this device of the so called Thouloss limit as a way of
kind of convincing people mathematically rather than because we needed it. It was much later that Nozieres wrote this nice
paper about the essentially, Fermi liquid limit. But itís obvious that at that point the phase shift is Pi over two and so
on. And you have unitary scattering, you have the Kondo resonance. There wasnít much else that we really did with it. In
that one we also made the point that there is a jump, we actually studied the analytic behavior of the phase transition in
that one dimensional inverse square and one dimensional Ising model which Thouloss at the same time and proved this little
theorem of his that there had to be either a jump or no phase transition at all. He proved the existence of that phase
transition and it was his thinking on that that led him to Kosterlitz-Thouless. But our argument for the behavior at the
phase transition is almost identical to the behavior at the Kosterlitz-Thouless transition, and it agrees with what David was
thinking at the same time too. But we derived this behavior within a true singularity plus a jump in the order parameter,
which is very anomalous and you only find elsewhere in the Kosterlitz-Thouless type phase transitions. Well, itís J Phys. C;
and people tend not to find it, but I thought it was a nice paper.
Actually I spoke with Mike Kosterlitz recently about this Kosterlitz-Thouless discovery and one thing he
mentioned was that, in fact, it was your paper on the scaling where he, essentially, learned to do RG and that they were able
to apply those ideas to the Kosterlitz-Thouless problem. So maybe we should turn to another topic. Why donít we move onto
some work on spin glasses and then perhaps weíll cover some other gaps in this period a little bit later.
When did you actually first become interested in the spin glass problem? You once told me that it predated
your time at Cambridge.
Well, it started out with (hidden here somewhere thereís a paper with Harry Suh) about superconductivity.
I donít know where that appears. We were worrying about these results.
Ď59, Spin Alignment in the Superconductive State.
Ď59. Really already there. Well Bernd had been worrying about these alloys of his, and he claimed that
there was what he kept calling it a ferromagnetic transition, he claimed that there was a ferromagnetic transition and that
it crossed the superconducting transition and I guess it was CeRu2+gd. And he had this characteristic temperature. The
transition temperature dropped down rapidly as a function of gadolinium. Cerium ruthenium 2 is simply a superconductor. And
then there was what he called a ferromagnetic phase transition going up to the right, more or less linear in concentration,
and we were interested in what happens when these two intersect. We made the obvious point that thereís a heck of a lot more
entropy in a magnetic transition than there is in a superconducting transition, and so we thought the magnetic transition
should take over and we should get low superconductivity below the magnetic transition. But in fact the superconducting
transition goes right on through. It stops a little bit and it may have a curvature there but it goes right on through and
remains superconducting. And so our first idea was well maybe we pulled a periodic behavior of the magnetism so the
magnetism will orient itself in domains which are small compared to the penetration depth but large compared to the magnetic
coherence length and regain the energy that way. But then we began to realize that the gadolinium in this compound wasnít
necessarily ferromagnetic anyhow. Bernd called it a ferromagnetic transition but it wasnít, but we didnít know what it was.
So that was one question about such things.
Another thing which came up, again, my ubiquitous journal. John Wheatley was infringing our patent on the Josephson
effect and making squids at SAT and he needed something to test his squids on, so he was studying copper low concentration
manganese alloys and he submitted the paper to Bernd. I think he thought it was too long to publish anywhere else, so our
entire last volume consisted of this long paper on squid measurements of copper manganese. Even though I edited the paper, I
didnít really notice it too well. He had an absolutely characteristic spin glass magnetization curve, so he was the first
person to observe a spin glass. That was published about Ď67, Ď68, something like that.
All this time I was saying to Bernd, ďThat isnít a ferromagnetic transition; itís something messier, and we donít know
what really is going to happen there.Ē And this funny little graduate student, Wai-Chau Kik, and she was scared of her own
shadow. Whenever she was talking to anyone senior, like myself, her voice, which was normally rather high, went up to a
squeak and you could barely understand when she was talking, not because she didnít speak perfectly good English, she was
from Singapore, but because she squeaked.
So she didnít overlap with Yuval, I gather?
Yes, she overlapped with Yuval.
The paper from Ď71 on page 12. Comments on the Ferromagnetic Theory Consisting of [???] Magnetic Alloys.
Yes, I think thereís an earlier one. Oh no. Thereís one in 1970, Materials Research. Localization Theory
in the Copper Manganese Problem. Well that was inspired by another thing, a Walter Marshall observation. Before we ever
knew about spin glasses we knew about the scaling law, that there was a perfect scaling law between temperature and
concentration, and temperature over concentration scaled perfectly in the transition metal alloys in precious metals:
copper, gold, silver. And that, of course, is just the scaling law for the Friedel interactions, itís 1/rcubed interaction.
It means that the interaction scale is proportional to concentration, and that these really were genuine dilute alloys.
So we knew that there were rather random interactions between the spins. And the very first thing I guess I ever did
was to think a little bit about this problem, the copper manganese problem. Copper manganese had always been a puzzle
because of this very old work by Charlie Kittel/Art Kipís group, the guy from Oxford, John Owen. Owen did a lot of work on
that, too, about how did relaxation happen in copper manganese, we knew that there was a Kondo model type behavior and part
of our bewilderment was that we didnít know about the Kondo problem and part of our bewilderment was we didnít know how to
deal with finite concentrations. And this was not really any better in terms of understanding how the spins polarize the
lattice. I guess we were beginning to understand at least how one spin polarize to lattice, but then there was this
concentration problem. So I said, ďWell, the manganese spins, you can linearlize the problem, and then you have, if itís a
quadratic exchange interaction you can find the Eigen functions and Eigen values of that exchange interaction and there will
be some first extended Eigen value of the exchange interaction and then you should have some kind of freezing into a
disordered magnetic state.Ē And I think thatís the content probably of this 1970 paper.
There was one other thing. We noticed that if you dissolved manganese in the crystalline lattice the susceptibility
tended to have a finite displacement, 1/chi vs T at a theta. But if you dissolved it in an amorphous solute, you found that
theta went to zero. There were some experiments about that. And thatís what I set Wai-Chao Kik, doing and so she did as her
thesis this little problem of thinking about — wait a minute. Where?
Comments on the Paramagnetic Curie Temperature in Amorphous Magnetic Alloys thatís the one where we showed
that in a crystalline structure you would get a finite theta and in an amorphous structure you wouldnít. So that was the
first paper. I guess the other paper has this wonderful title which contains the word spin glasses which first appeared in
print there, and Iíve always had an argument with, or when he was alive I had an argument with Brian Coles. He thought that
he invented the term and I thought that I invented the term, and I at least, had got it in print first. So I mentioned the
fact that there might be a random frozen structure there for the first time.
Just to understand, in this paper, though, you were trying to relate the spectrum of the bond matrix as it
were to the metal insulator.
Yes. I made this argument which I later made for localizing bosons, that you couldnít have any localized
states. The localized states would be killed by the non-linear terms in the interaction essentially by the fact that itís a
sigma model that the spin can only get so big, so that any local Eigenfunction would displace alright, but then it would
displace to the point where it ran up against non-linearity and would be pushed down into the continuum until finally you got
to an extended state and then you could have a phase transition. So I was still searching for this phase transition of
Berndís, more or less, in this discussion.
When did it become apparent to you that what you were looking for was a phase transition from a—
I was puzzled. In the early work, in the work with Suhl, if you read it, itíll be clear that I was puzzled
about why there wasnít a phase transition, actually. So all this time we were going on under the mistaken assumption that
there was no phase transition, so we didnít have a phase transition, although my eye had passed over and failed to notice the
unequivocal evidence from Wheatley that there was a phase transition. I just didnít read that Wheatley paper. I guess I was
so miserable about the journal and I didnít like to read things, I blanked it out.
So then when Nella and Mydosh did their AC experiments which indicated a phase transition.
I was all-ready, I was happy.
You were ready to go on that. As I understand it, there were many people in the community who had quarrels
with their data because of possible experimental problems, but you never seemed to have any problem with that.
No, I never had any question about it. But what was crazy is that I didnít look back at John Wheatleyís
data and say, ďWell, heís obviously right because look at John Wheatleyís data.Ē The difference between Mydosh and Wheatley
is just this. Mydosh was a peak and Wheatley was the field cooled case because he couldnít use a big field, he had to cool
it in the Earthís field, or in a low enough field so he could use the squid. So his was a temperature run and it was flat.
In this work with your student though, this was sort of a high temperature approach that you were trying to
Yes, that was a high temperature. That was strictly high temperature. I didnít want her to get messed up
with this real mess. Sheís still in physics. Sheís still teaching physics somewhere in the Malaysian area. She went to
Malaysia, got kicked out because of their anti-Chinese regulations and went to Singapore and I think sheís fairly happy
Then how did you start your discussions with Sam Edwards on this topic?
Notice that the famous AHV also mentions spin glasses. I was definitely thinking about these frozen
states, and I was assuming they were glass like and that there was no phase transition. But letís get to that later.
The first amorphous magnetism conference, Hooper and the notorious DeGraff editors, DeGraff is one of the stupidest men
Iíve ever had to deal with, and for a long time he ran all funding from NSF for material science, and thatís when we began to
realize that we had made a mistake in moving from physics to material science because he really loved good old fashioned put
the metals in a pot and metallurgy much better than he loved fancy metal physics. But the first place I met him and realized
his stupidity was at that conference where I did something on topics in spin glasses, and I think I gave Wai-Chaoís thesis
and a couple of other ideas I had. But I just didnít say out loud, which I should have, Iím surprised there isnít a phase
transition. But you realize that this original paper, spin glasses, if itís implications were followed out, would have said
there was a phase transition. But this continued puzzling.
Now where do we get back to? We donít get back to spin glasses until Edwards. Well, Edwards, I sat on the committee.
We had to replace Otto Frisch and who else had retired? Maybe it was even Mottís retirement. No, it wasnít Mottís
retirement. Pippard had moved over to be Cavendish professor so we had to replace Pippard. So I sat on that committee, and
fortunately we got Sam Edwards to take the job. I sat on another committee where I got completely blind-sided by Pippard for
which Iíve never forgiven him. He hired a man named Cook. Cook was a man whose contributions could not be found in citation
index, and Brain Pippard had the Cambridge snobbish attitude towards citation index that if you have a large number of
citations, you are somehow common, lowbrow that the real physicists never published, they just talked to people. And so he
brought in this guy named A. H. Cook and his contributions, if any, were mixed up with two other A.H. Cooks, one of whom had
an E on the end. I thought that I had no problem with this appointment going through, and it made no effect that there was
no citation contribution to science, so he was appointed. I should have stalked out and said, ďIím never going to darken
your door again,Ē except I was about to do that anyhow. I didnít. I didnít make the fuss that I should have made. I feel
very guilty about that because I should have got John Rowell that job, but I did get Edwards in. There was some question of
Michael Fisher. Iím not sure we shouldnít have done that, I donít know. Michael hadnít applied, and we thought that for the
Cavendish chair, the people should at least have the grace to apply.
This was when Pippard was appointed that Michael Fisher visited?
No, when Edwards was appointed. It was a theoretical job because Mott had gone as a theorist, even though
it was nominally the Professor of Experimental Physics, he was seen as a theorist.
That canít have been the Cavendish professorship. Much later he got the Cavendish professorship when he
came back to Cambridge.
Yes, he got it much later. He got Pippardís professorship, I think. I donít know whether it was Pippardís
or Frischís. It was one of the old, established professorships. But he was still head of the SRC, the equivalent of NSF.
So he took the train back and forth to London, stayed in London during the week and Saturday mornings he showed up for coffee
in the Theoretical Physics Department. Volker I guess for some reason didnít apply for that job, but did get a professorship
when I left. That may even have been fixed up, Iím not sure.
Anyhow. Sam and I talked about glasses and spin glasses and so on, and Mydoshesíresults were just out. I said, ďLook,
weíve got some data now. There is a phase transition.Ē And so he and I together worked out the first half of his paper,
which was essentially a little self-consistency argument that showed that there could be this order parameter Q, and that
just self-consistent mean field theory would give you a temperature at which Q would survive without anything fancy about
replicas. But then Sam figuratively pulled out of his back pocket this replica method that he had been trying to apply to
gels for many years and had failed. Well, not failed, but it just didnít seem to work. Said, ďWell, maybe this will work.Ē
So he worked it out on the train back and forth to London and came up with the answer. I had essentially drawn random
potentials on what we would now call random landscapes on the board and said, ďThe essence is youíve got this random
landscape and how does the system respond to it?Ē And I got this argument that it should find an extended state and freeze,
so Iím happy that thereís a phase transition, but we need a formalism, and he suggested this self-consistency formalism and
that worked very nicely. And that gives you this kind of self-consistency, except itís a Q-squared over T-squared instead of
a Q over T that comes in. Otherwise itís the same thing. And that was it. We published it before he ever arrived in
I had been quite unhappy with Pippardís being chosen as the Cavendish professor. Heís such a pessimist. He had this
English attitude. I guess itís conditioned by wartime or something, that if things are going to be bad, letís accept it and
letís really make the best of it rather than things are going to be bad, that means youíve got to fight to improve them. And
he said, ďOkay, our students are not being used by UK industry. The good ones are going overseas. So letís train them for
UK industry instead of training UK industry to use our students, letís train the students for UK industry.Ē And this kind of
thing drove me absolutely up the wall. We had a beautifully organized syllabus which was based on statistical mechanics and
quantum mechanics, and you could do whatever else you liked around them, and we taught a lot of condensed matter physics, a
lot of classical physics and so on. But we really did feel that any person who calls himself a physicist should know quantum
mechanics and statistical mechanics. And he was determined to destroy that. So I finally decided Iíd go back home and John
Hopfield seemed eager to see if he couldnít get me into Princeton, and so I went back home. So that was the last paper we
wrote in Cambridge.
Actually a question about this paper. Itís always struck me that a conceptual underpinning of the replica
trick is the fact that disorder induces interactions. Could you comment on that?
Sam had always had that point of view. Yes. Sam had, in much of his earlier work where he was trying to
do the localization problem, he would do it with his favorite path integrals, and then if you average over interaction you
get interaction between paths so there is a precedent of n Ď 0 trick. And deGennes has an n Ď 0 trick thatís based on that
rather than the other, leaving the loops out of diagrams. But Samís was much more formally based on this limit and going to
zero in replication, and actually the motivation from our point of view was this self-consistency method, which doesnít
require replicas at all. It says, Letís do it once and then do it twice and see if thereís a correlation between correlation
out in the background in the mean field, how much correlation can that induce in the local spin?Ē So in a sense itís that.
But itís not motivated really by the interaction trick. That seemed to just not work well. Thereís some wrong papers
in here that I did using that kind of approach. This paper with Bob White, Diamagnetic Enhancement, this paper about sizes
of the localized states in the mobility edge, PNAS, they are both wrong and they are both based on that kind of approach. I
didnít like them and it was just a wrong way to think about localization. Now, of course, people do localization with the
replica method, but it was a long time before you could do as well with the replica method as with diagrams or with my
methods. So I was kind of negative about that approach because Iíd seen it fail so often. Sam was all for it, and seemed to
me to be doing it in a sloppy way and he used it in trying to calculate in some of these poor calculations of densities of
states, for instance, some of them diagrammatic calculations which the CPA had replaced. CPA being obviously better. So I
didnít really like it. I knew that existed, but I didnít work in that direction very much.
This is a good place to stop.
Well thank you. We learned a lot.
Session I | Session II
| Session III
| Session IV