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In footnotes or endnotes please cite AIP interviews like this:
Interview of Philip W. Anderson by P. Chandra, P. Coleman, and S. Sondhi on 1999 October 15, October 29 and November 5,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Interview focuses briefly on personal details of Philip Anderson's life and almost exclusively on technical aspects of Anderson's research. After discussing his undergraduate and graduate education at Harvard including his research on spectral lines, he begins the technical aspects of the interview by reviewing his interest in anti-ferromagnetism and his time in Japan. Included in this are his thoughts on the organization of the Japanese scientific community. The second half of the interview deals entirely with his interest in superconductivity and localized moments. Within this general topic there is some treatment of his thoughts on the time that he spent in Cambridge, MA.
So Phil, let’s start off by asking, at what stage did you become interested in science? Could you tell us about some formative influences?
I can’t remember a time when I wasn’t 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 don’t remember who they were by, but what I do remember is that the opinions expressed there were terribly old fashioned and now are all obsolete, but they fascinated me because they tried to explain. They had a picture of this pile of clay which you squeezed and mountains came up, and things like that. No, I can’t remember when I wasn’t. If I could interject something, one of the really big influences in my life is very simple. If you remember Shaw’s 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 Osbornes, always got A’s and I 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. So I can’t remember when I wasn’t 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 didn’t blow myself up. And he encouraged me to collect butterflies and to identify plants, things like that. So there was some encouragement, but I didn’t need much.
Do you feel that the science education that you had in school helped you towards developing your interest in science?
Well, I can’t really quite ask, “What science education?”, 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 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, couldn’t 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 there were admissions requirements for the school. (and a ridiculously small fee) At the grade school I think the main thing was resistance to whatever they did to us, but 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, what’s important in people’s 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 sense or whatever. We weren’t. 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 kind of mascot-she was younger). It was her mother that was important because her family had the only, probably the only really good hi-fi in all of Urbana, Illinois, we had tried to learn classical music from the public broadcasts, which were just awful in those days. We’d go there and listen to records and we’d 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 John 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 wouldn’t 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. Then we vacationed with this group, spent three summers in the Tetons, and I remember we met some of them in Northern Italy the 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 members 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 didn’t do quantum mechanics. He made it into a leading department. He just basically took any graduate students Fermi had and hired them. And then when he realized he couldn’t 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. That’s 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 you’ve [???]
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 he’s the one who took the millions of dollars that he earned and quit, retired too... 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 he’s 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 didn’t have the personality that attracted people, so instead he would spout radical slogans. And eventually he grew into radicalism. I don’t 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. It’s not that he wasn’t 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. You’ve 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?
13. I appreciated a lot of things. At least more than what I would have been expected to, although I didn’t 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. We 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 experiment 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 didn’t 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 didn’t 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 internment 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 can’t 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 didn’t control the student body. But the Eastern prep 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 wasn’t that much. The rest was paid by scholarship. So I wasn’t 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 naïve 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 on Wheeler Loomis’ advice. 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 didn’t 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?
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…
Who taught the course?
Wendell Furry. He was a wonderful teacher. Everything about him 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 couldn’t 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 Pierre’s 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, myself, Henry Silsbee, 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 wasn’t. It was Tom Kuhn, and Bob Houston was brighter than Tom Kuhn. And Henry Silsbee. 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?
Really, none. 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. We’d 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, “You have glasses.” 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 you.
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 fathers who knew about Los Alamos and other things, and some of us had other sources 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, not one of the really high ranking kids. And Henry Silsbee knew about that. He stayed in physics. But I didn’t. My physicists friends back home in Urbana kept absolutely mum and didn’t advise me to stay in physics and work in nuclear physics, and so fortunately I didn’t. 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 you’ve 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 couldn’t 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 theory 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, Euler’s equations and all that kind of stuff. (He was running the Harvard branch of the Radlab.)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 didn’t go into that. I got some hints just in the problems. I derived from my book Maxwell’s distribution, which I was thrilled when I could derive Maxwell’s distribution to really understand how a gas worked. That was a big thrill. But I didn’t realize the whole thing had already been done. There was no awareness in undergraduate school. I learned about real physics in an 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 couldn’t keep his mouth shut about anything. I never supposed 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 I would read it, and that had quantum mechanics in it. That was a thrill. We didn’t 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, “I owe so much money, you can keep the book.” I still have it.
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 wandering around Washington museums, all sorts 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?
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 we’re on the topic, because we somehow skipped it, could you tell us a little bit about your sister?
Well she is older. She’s 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 wasn’t my sister’s style. She was very much a tomboy. When we had a carpentry project, she was very likely to grab the hammer from me and say, “Here, let me do it,” 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 mother’s 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 WAVEs. 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 didn’t 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 don’t think he was punished for that. He didn’t 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 Company’s 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 growing up?
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 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 let’s 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 I’d 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 that the Naval 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 we’d get enormously long propagation over water and things like that. So I looked at it and I thought, “This kind of thing I can develop happened at Harvard.” Really interesting stuff, and I wanted to go back. You can see I wasn’t very imaginative. I went back, slept on Tom Kuhn’s couch, and Van Vleck said, “Fine.” So I came back. I was discharged in October and one week later went off for my Ph.D. Schwinger arrived in, let’s 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 talked about 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. He’d 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 partial differential equations 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 Revs Modern Physics as our textbook. Furry taught out of Pauli’s 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 didn’t even understand physics, so it wasn’t much help. So we learned German. The next year I took Group Theory from Van Vleck, and I still have 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 Hildebrandt but he was busy worrying about the elastic properties of bomb 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 elasticity 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 “Fun with the Variational Method.” 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 was... I had two very good approaches to solid-state physics, neither was solid-state physics per se. Gorter came and told us all about magnetic relaxation. 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 didn’t do statistical mechanics, Furry did kinetic theory. 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, Lew 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 Tom and I took analysis together. It was an awful course by a mathematician called D.V. Widder in which he undertook to do all of complex analysis without ever doing a single contour integral. 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 Kuhn and I worked very hard. We would always look at the grades on the homework papers, but we had 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 he’s 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, “Oh my god, what was that?” It could have been something bad for all we knew.
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 — Bainbridge’s first mass spectrometer. He had an oil drop experiment, I don’t 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 and did NMR. He became a particle physicist. 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 Ken Wilson’s father, E.B. Wilson in microwave spectroscopy. So we didn’t differentiate. All of us who could manage had Schwinger’s course together. I made my choice because I kind of liked 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 wasn’t 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 learning about my friends who were doing microwave. So I guess when I went and saw Van, I said, “Well, have you heard about the good things with microwave spectroscopy? Maybe I’d like to do something with that.”
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, where anyone had made any effort to do a quantitative job; this 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 in line broadening because he actually thought about how the forces 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 didn’t pay much attention. I didn’t worry too much about it in the thesis. But you know there were literally thousands of new data in this field. Before the war 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 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 a sudden we had coherent sources and we could study a line by taking the frequency of our 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 Wilson’s 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 quantum 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 names to look up for 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 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 a training job in the new 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 bursar’s 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, “Are you doing anything?” and I said, “Well, yes sir I have been,” and he said, “Write something up for me.” So I quickly wrote up a few sheets of paper, and on the cover I wrote, “Dear Van, you old bat,” 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 ‘48 and we typed it all out in the fall of ‘48 and then went off to Bell in ‘49.
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 wouldn’t 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 emitting because that frequency modulation starts out with a new phase after the collision. 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 in a gas. There is very little vibrational degeneracy, so you’re 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. That’s 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 of the interaction in 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 Schwinger’s course because he taught me about how to use the unitary time development matrix, 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 lineshape? 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 used a classical path approximation, and realized that what I needed was the correlation function of the dipole moment. 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 Waals’ 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 the results. The only thing is I said, “Well, these two lines he got wrong.” 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, “Well I’m sorry I got these two lines wrong,” and he laughed at me, and he went back and measured them and indeed he had been 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 couldn’t be telling the great Bleaney that 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 wasn’t afraid.
The totality of the data that you explained was that presumably there were systematics for the gases and different things?
Yes, I did that ammonium spectrum I did, I think with a rare gas. For infrared I’d get a couple of the classic vibrational lines that had been done in old- fashioned spectroscopy. And then I said, “Well, I’ve done it in principle. I’ll do a couple of others.” 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. Original proofs without knowing it. I was using fluctuation- dissipation theory without knowing it. Well, there wasn’t 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 can’t measure that in the microwave region. Just take B over A and that will be part of the induced absorption. So I was doing that. 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 of the dipole moment of the whole sample. I was kind of fascinated by that. I remember Joyce asking me, “Well you’re doing this very niggly little problem that seems very, very specialized. What general meaning does it have?” and I said, “Well, I can really understand what’s going on in a real sample of gas.” 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 at all?
Not really, well, I’d heard me of it in his course essentially. I don’t 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: I met him later in Berkeley which is of course where the project for high school education came from. So he and Schwinger had done some work along 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 Schwinger’s 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. But no, the general formalism was later — I was basically the first.
So what happened in solution to this problem from the time that you ended up at Bell, how did that go?
(There were two — many — papers by chemical theorists about my methods.) Well, I went to Bell twice. The first time was during the 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 about 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 didn’t go to married students.
Could you elaborate on that for me?
I don’t think in those days you got married and went off to a post-doc. You postponed what plans you had until you’d 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 but I couldn’t 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 didn’t finish half of my Ph.D. so I didn’t 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 didn’t disagree because I admired Bell enormously. But I went there and I didn’t 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 sort out the problem and see how the interactions affected the line. I couldn’t say I had solved the problem. And they were very polite to me and I 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, like Charlie Kittel, but I didn’t impress them. 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 couldn’t persuade his management, Harvey Brooks that I was worth hiring, so Harvey Brooks turned me down there. Sam Goudsmit turned me down at Brookhaven for the reason that, when I was asked what I wanted to do now, I said, “Well I finished my thesis. I want to do something else.” And he said, “This man can’t have really done a very difficult thesis if he finished it.” Well the fact was I had creamed the thesis. There was no more obvious 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 expedition when he was at Harvard. He turned me down. Westinghouse wanted me because Ted Holstein was there and he had been interested in what we’d done. But Ted couldn’t 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 was 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 wasn’t the University of Washington; it wasn’t 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 in and said, “What do you want to do?” and I said, “I want to go to Bell. It’s got Bardeen and it’s 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 they’re working in my field. I want to go to Bell.” And then Van went to Bell, on the Phoebe Snow (the Lackawanna railroad’s crack train). It is not an apocryphal story. He actually did ride in the cab 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 in Boston and interviewed me, and he said would I work as a post-doc for him, they didn’t have any room for regular jobs and I said no, and he said, “Well we’ll hire you anyhow.” And of course I didn’t 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 don’t 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 can’t 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 wouldn’t have exposed himself to Schwinger and Weisskopf... And I think then when he decided on the thesis committee he decided he’d better find out where I was going to work.
How did your thesis defense go?
They just didn’t 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. That’s when I said well we should think about social groups. In the first place when I arrived, we were two people over what’s called nose count. 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 Matthias, 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 didn’t 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 wasn’t too important. (I guess I didn’t mention taking the radar course yet at the Naval research lab). But very soon, I don’t 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 Townes’s molecular spectroscopy. He also did a lot of preparatory chemistry for later work in magnetic resonance. But there was this little group, and 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 Matthias 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 grew, what their quality was and so on. I remember people joining us, and when Hal Lewis came, which was a couple of years later, there’s a complicated history involving refusing to sign the oath in California. He was going to the Institute and going to Bell Labs where we didn’t 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 didn’t 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 “security” questionnaire sent to all of the people at Bell Labs, Gregory and Alan and me. So that was part of my socialization and it was very useful for me because I didn’t know beans about either solid 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 we had 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 lab’s bridge tournament. And well there was really no problem with socializing. I mean we worked very well, had the journal club, politics, 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 Bernd’s work on ferroelectrics; I wasn’t that interested in Bill Shockley’s ideas on ferroelectrics, but I was interested in what he was doing. I was interested in the magnetic resonance work that was just being set up 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 Shockley’s ideas on ferroelectrics, and honestly did think about ferroelectrics and in particular with Gregory we thought hard about phase transitions. Gregory was obsessed with Onsager’s work in the Ising model. He was in some ways a little undervalued]. 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 that’s 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, Walter and Quin were part of this gang of people. It was interesting that 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 Labs.
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 together?
Well, Gregory really was the instigator of that. He and Richardson went to a conference on phase transitions that I didn’t go to, and when they came back 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 to be where the free energy became unstable to go over to another phase. It was very similar to Ginzburg-Landau. We didn’t 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 doesn’t satisfy this transition theory and they got to talking to me, and I said, of course it doesn’t, 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 doesn’t work. And I think this is maybe the first published reference anywhere that says, because of Onsager, the standard theory doesn’t work. Now Gregory knew that, so it actually wasn’t because of Onsager, it was because of Kramers-Wannier, because Gregory had deduced from general arguments that in fact they have a symmetric logarithmic specific heat. a logarithm that diverges. That predated Onsager and that was Kramers-Wannier. And so we looked at it and we decided, well, the free energy wasn’t 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 isn’t analytic. And I think this was the first published version of that. But it’s 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, “There is this new thing called anti-ferromagnetism. Are you interested in it?” And Gregory was interested in it because he thought, “Well, let’s do an Ising model with anti-ferromagnetic interaction,” and he realized that for the square lattice it’s the same model because it’s 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 antiferromagnetic, if you drew atomic radii for MnO, you have a great big oxygen, making the manganese quite far apart. So I set to work to think about Kramers’ 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, superexchange number one. There is this Neel paper about anti- ferromagnetism, and then we discovered Van Vleck’s old paper. I said, “But of course if exchange interactions are the way that Kramers’ 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, the 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 Shockley’s 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 Charlie’s 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 ‘30s that you can get any ratio of theta to TC 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 could 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 I’d 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 Bardeens, an awkward evening sitting at the card table and four chairs.
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 don’t know. Somebody reported, maybe Charlie again brought it to my attention. I don’t know. I must have read Martin Klein’s 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, “What about spin waves and interferromagnets?” 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 Klein’s 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 ion 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 interpret the function. Martin Klein had taken that proto-theory and said, “Look, it even fits in the case of ferromagnetism if you do the quantum mechanics right.” Except for a smidgeon, including the zero point fluctuations of the spin waves makes the classical theory of ferromagnets the same as the quantum theory of ferromagnets. We realized, “Ah, you have to do anti-ferromagnetism,” 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 Weiss’s theory where he had tried to do classical cavity theory on anti-ferromagnetism and he got an answer which didn’t make sense. So I realized how the quantum theory didn’t work because it had a divergence in the zero point fluctuations. And that was the other paper that became important because of the ground state. But I had been thinking, “How does Weiss’s cavity theory compare with classical?”
What was Weiss’s 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 we’re convening again for the second time interviewing Phil Anderson now for his period at Bell Labs in the ‘50s. Phil, last time we spoke we’d been talking about your note with Gregory Wannier and Richardson about the realization that mean field theory wasn’t 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 didn’t know at all what he was doing.
This was Misner, Thorne, and Wheeler?
I guess it was Misner and it wasn’t 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 essentially the same models that eventually Ken Wilson used to actually solve the problem, essentially Phi to 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 didn’t 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 didn’t diverge in five dimensions. We weren’t as smart as Pokrovsky and Padashinsky who realized that they could be converged logarithmically in four dimensions. So we didn’t get that far, but we did show that they didn’t 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 didn’t succeed. That’s just a lot of stuff in notebooks, but there was an interest in this general field and realized that things hadn’t really been properly solved, but I just wasn’t able to do much with it.
Thank you. Just as an aside, actually, you mentioned diagrams. What kinds of diagrams did you draw, Feynman diagrams?
Well the diagram series had very legitimate classical foundations in the idea of cluster expansions. Gregory Wannier had essentially pioneered that particular art. He at least realized that Mayer’s diagrams that he used in classical statistical mechanics were essentially equivalent to 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 wasn’t 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 wasn’t 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, “Statistical mechanics is easy, and so I’m going to do kinetic theory,” 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, Conyers had already seen the relevance of the free energy undergoing a singularity and breaking into a two -well potential and so on. He’d 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 don’t think there was anything that wasn’t 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, let’s 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 let’s 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 don’t think we got as far as your work that’s 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 don’t 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 hadn’t seen the relevance to what we would now call broken symmetry. He really hadn’t realized how all of that went and he hadn’t 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 didn’t think what the more general context was.
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 didn’t even really want to go. Japan was obviously still recovering from the war. It sounded like a very difficult adventure. I didn’t know enough to realize that this was a come on rather than otherwise, so I said, “Well, maybe I’ll come next year and maybe only for half a year.” And by return mail they said, “You’re on. You’re coming next year for half a year.” So we 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. I’m 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, I’m 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 didn’t 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 separate.(Note, at this point I was a bit annoyed about my questioners’ ignorance of my work on exchange narrowing etc., which really was as important at the time, or more so, than the AF work — and still has relevance, eg in cuprates!)
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, “Well, I practically discovered you,” he said, “No, I discovered you.” 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 got there.
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 I’m 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 slave equations. I guess Kirkwood was also on that panel because he’s 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 didn’t they just use the fluctuation dissipation approach and get response functions as correlation functions of the relevant operators, relative moments and so on, and we’d 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.
I’d 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 there’s 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 Schwinger’s, 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, “Look, molecules don’t have dipole moments.” And I thought, “That’s odd.” 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, Bethe’s original paper, Waller’s paper doing numerical calculations and verifying Bethe’s results, and some of Waller’s papers. There was a Kramers-Kastelejn paper in which they had been trying to do two 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, “If you just average over all possible directions, in some sense there has to be a singlet in there.” So he had some understanding of these difficulties, but he never wrote it down either. 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, “But people must realize these things, people must know these things. All our seniors are very much brighter and wiser than we are,” people like Pauli 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 find out whether anyone knew anything about that, and as far as I know, they didn’t. I don’t 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 don’t know, I guess I didn’t look up the deBye-Waller factors and things like that. I think deBye-Waller merely assured themselves that sums converged at zero at the low end and then ignored the question of exactly how it happened.
What about in ferroelectrics?
No, I didn’t think about this in connection to the ferroelectric because the ferroelectric wasn’t really a quantum phenomenon.
One more connection I’d 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 forward a bit and let’s 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 experimentalists 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, which we called POV because in Landolt-Bjornstein, it 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 it’s 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 I’d been at Harvard I knew about 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 qualitatively 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, Waller’s moment method 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 isn’t all that important (2014 — Too modest!), 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 I’d 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 didn’t 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 don’t remember. But eventually the result was what they called the Little Red Book, of which I have some copies.
Well, I see your magnetism.
That’s 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 talk.
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 don’t 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 in the 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 a bit 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. Kubo’s 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 Kubo’s 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, and that did count as Bell service. 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 were on the order of 50. 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 didn’t, for instance, have lots and lots of more surplus equipment lying around that could be immediately applied the way our people did it.
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.
That’s a fairly long way ahead. Let’s 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 we’d 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-fine 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 quantum 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 as 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 Suhl’s study of the nonlinear effect 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 it’s 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 I’d always been a little interested in that. Well, I wrote one experimental paper actually about magnetite at one time, and I’d 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 wasn’t 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. He’s a very tough guy. He’s 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, “You owe it to me,” 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, that’s the interesting thing. He’s 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 it’s 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 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 wouldn’t see any of these spin packets). Low density you would see all spin packets. Intermediate densities, you would see the phosphorus appear to have a spin and a half, so you’d 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; we’re too close to the density where they’d all collapse. It wasn’t a gradual change from a localized to an extended state; it was an absolutely sharp change. 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 don’t think young people nowadays or many people ever learn, which is that experiment can tell you theoretical results. Experiment is often so unequivocal, so simple and straightforward that it tells you what’s 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 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 there’s some interesting things having to do with the orders of the scattering, orders in perturbation theory of the scattering. It turns out the anomalous Hall effect is in principle independent of scattering, it’s in the order of tau/tau, so you could easily make mistakes. Smidt managing to produce a Hall effect in a 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 “cisport” 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 very formal, very pecking order. Since I’d 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 didn’t 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 that’s not to be discussed here. But of course I didn’t 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 weren’t 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, “Well, you take the hydrogen atoms farther and farther apart and then eventually the electrons will localize on them because of the Coulomb interaction.” 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 wasn’t 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, you’d 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 a while and so on and so on and so on.
What summer was this?
‘56 and ‘57. 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 it’s 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, Quin’s was that it’s obvious and Walter’s was that it’s impossible, which is fairly characteristic of both of them. And so that was when I knew, as I told it later (probably it wasn’t 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 don’t 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 in powers of the scattering using the kinetic energy as the H0 and the scattering as the perturbation, so I said I’ll do a cisport theory with the scattering as the unperturbed energy and the kinetic energy as perturbation, and showed that perturbation can converge. I don’t 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 hadn’t 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 that’s basically the Kolmogoroff idea having to do with long tail distributions that you can deal with just keeping the largest term. Which I don’t know if it’s ever been proved as a theorem, but it’s certainly true because it’s 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 Spencer’s 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 qualitatively 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 weren’t important because that’s 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 that’s the Lorentzian long tail distribution. It’s even more so in these things like what I did with Jim Talman. It’s one of the papers here, Pressure Broadening in Spectral Lines at General Pressures, and there’s 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 wasn’t 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 there’s 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, it’s 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 — no idea who? Claudio Simon?), I don’t know whether that’s true because he’s doing perturbation theory, and there’s a problem where perturbation theory is very dangerous because it’s known that conductivity doesn’t self-average adequately. I didn’t 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 theory 0f 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 didn’t know what to do about interactions. I thought for awhile about what to do about interactions, and it wasn’t 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 didn’t really see what to do next. But he passed this whole problem onto his student Meir Weger, our post-doc Meir Weger. Meir Weger, if you know him, you realize he isn’t the easiest person in the world to work with, and George got interested in other stuff too, so it wasn’t 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 for 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 in.)
The other thing, of course, was that Mott and then Thouless brought in the concept of the conductivity, and I hadn’t 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 you’ll find a footnote in it that says, (P.W. Anderson has proved that this is gauge invariant.) So it obviously wasn’t the publication of the paper. Well, Leon (and that was one other name) Leon Cooper was one of our summer visitors. I don’t think he was there very long, but he certainly came and talked and he visited the institute and talked down here. I don’t 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, that’s unlikely. There wasn’t 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 don’t remember who everybody was, but everybody did talk about it and we were very interested in what he had to say.) But we didn’t know what to do about it, and obviously he didn’t directly explain superconductivity. There was a lot of skepticism, I vaguely remember, on Walter’s part particularly about the fact that you could very easily produce logarithmic singularities using the Fermi surface and that very often they weren’t there. Later on he formalized this with his theory with Kohn and Majumdar, showed that impurity doesn’t do anything at least to the free energy, even though if you just took the impurity’s effect on electrons it wouldn’t always have a bound state. So all of us knew that this is a very tricky question and mostly the Fermi surface doesn’t appear in anything. We didn’t 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 superconductivity.
When was that?
That was in ‘50 or ‘51. And by the time we were in Japan there was a Japanese paper more or less showing that it wasn’t true, and Frohlich was there, too, and Frohlich admitted more or less that it wasn’t the theory. Bardeen was still being stubborn as I remember from 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 Mendham. 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 didn’t say this, he didn’t say a thing about the theory of superconductivity, but I later realized he was in a bad temper because he was being interrupted. But that’s 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, “Well, hey, we could recast this BCS theory in terms of spins,” or Harry decided that he could. And I was interested in it and I looked at Harry’s spins and said, “Isn’t it interested the electronic state in terms of Harry’s Spins looks like a domain wall,” 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 couldn’t be the right theory because it wasn’t gauge invariant, but by this time I’d already convinced myself it was the right theory because it was another case where experiment tells you what the theorists don’t. There was no question the experiments were 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 an 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 collective 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 that’s 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 didn’t 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. That’s 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 weren’t spin waves, there wasn’t a collective mode.
So your realization that there was no order parameter to that would be the summer of ‘57?
Yes. Well, there were various other things in that original — I don’t 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 superconductivity.
Yes. Well, there’s 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. There’s a lot of stuff having to do with impurities in superconductors. I did everything but do the right theory, which was Abrikosov-Gor’kov. 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 don’t need to go into detail. But anyhow, that involved Charlie Kittel’s 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 it’s wrong and what’s 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 didn’t 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 couldn’t 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 didn’t explain Galt’s effect. I felt very guilty about that because Galt’s effect did turn out to be a very interesting piece of work. He was seeing the Az’bel-Kaner resonances in a rather difficult regime in which to interpret them, but they were very relavant to fermiology and the bismuth samples he was looking at. But I didn’t have the foggiest idea what they were; I just knew they weren’t 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 he’s 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 (three?) years visiting him in the summer on his Union Carbide grant that he’d 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 — Jim and I were walking around the campus one day and he said, “Why don’t impurities effect superconductors?” And I thought for about a microsecond and said, “I suppose it’s because of time reversal invariance,” and then I thought for another considerable number of seconds and I said, “Well, I can fix that. I can do that.” And so I invented this kind of scattering representation. I don’t know that you’ll 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 didn’t think it was a very important paper. It was that new journal, and I wanted to encourage them, but that’s 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 Knight 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 I’d already had the germ of the idea that super-exchange was due to the Mott insulator effect, but I hadn’t known how to do it quantitatively and I listened to Leslie Orgel’s series of lectures just out of idle curiosity and then said, “Wonderful, I can actually do the whole quantitative theory of the wave functions and their overlap integrals and super exchange.” And so that’s 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 hadn’t been with the first group that went, the first group after the thaw. His colleague Kip had gone and I suppose that’s why he was asked to the second group that went to Russia.
Now this was the summer of ‘58.
The summer of ‘58. We didn’t have much time, but it was December of ‘58 that this meeting was and I said, “I’ve got this old work in my notebooks, I can talk about that. I’ll go.” So we were the second delegation of solid state physicists to go to Russia that winter. Again, I ascribe this to Charlie’s 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 I’d 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, Gor’kov 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, ‘56 and ‘57. There were also Schwinger and Martin, but Ward and Montroll was perhaps more complete than Schwinger and Martin.
Actually, that’s generally not in the literature. Schwinger and Martin are characteristically credited with —
But it’s published with —
I meant the referencing.
Yes, it’s not referenced, but it’s 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, it’s not clear whether Matsubara or Kubo or both are responsible for them.
When I asked the Russians about this, they said it’s not in Matsubara’s papers at all, actually, so the Russians claim that they discovered it independently and couldn’t agree on who to name it, so they put Matsubara’s name on the frequency, but that’s the story I’d heard from Gor’kov because I’ve just heard your end of it.
That’s interesting because when I was in Japan in 1954, ‘53-‘54, Kubo had already invented the periodic imaginary time coordinate and I said, "What use is that?” One of the cases in which I really was notoriously wrong about something. [laughs] I said, “That’s just formalism, for God’s sake.” Yes, Kubo actually is the discoverer of the —
There’s 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 hadn’t taken that, but it’s 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 doesn’t 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 wasn’t 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 he’d found what he called ferromagnetic transitions. Now Bernd Matthias doesn’t know a ferromagnet from a hole in the ground; he’s not at all interested in order parameters, symmetries; he couldn’t 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. It’s quite a wrong paper. Well, not wrong, but it’s quite a naïve paper about this problem, but it’s interesting because it’s 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 it’s connected to the work of superconductors that we’ve been talking about, and that’s 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, it’s 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 ‘58, 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 he’s manic-depressive and if he would work for too long at particle physics he would go into his depressed phase. Well, it’s 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 Bernd’s 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 ‘61 when I was there. Jeffrey Goldstone was there, and Steve Weinberg was actually there in ‘61. 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 the Goldstone theorem and I said, “I can fix that. Goldstone theorem doesn’t hold in superconductors.” So it was only after having heard of the Goldstone theorem I wrote this paper to say Goldstone theorem, schmoldstone theorem. It’s okay. You don’t 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 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, “We want to make theories in particle physics, but we haven’t gotten enough massless particles,” 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 Schwinger’s and referred to it, but it had absolutely nothing to do with my line of thinking. I don’t know whether it’s right. I suspect it is right. It’s kind of a general, very general argument that there’s no particular need for a Goldstone boson, rather than a specific model that will give you the Higg’s 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 ‘63 is simply that I just sent it in as an ordinary paper and they had about a year’s delay. I don’t think there was referring delay. I wrote it in the summer of ‘62 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 didn’t 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-Mills” because that was a problem that was obviously there starting from the end of this paper. So, clearly by ‘63 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, doesn’t it?
And there’s super-exchange.
The super-exchange must have been in ‘58.
Well, the theory occurred to me in the spring of ‘58 and I was working on it in the summer of ’58 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 didn’t 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. We’ll 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 into 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 I’ve 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 I’d never heard, I realized that actually Brout and Englert had a fairly considerable influence on the whole development and must have gotten their original 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 t’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 ‘62, which does seem, looking back at it, to embody the Higgs mechanism in rather final form as a 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, ‘61. Could you tell us something about them?
Well, actually in my notebook you’ll 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 wasn’t aware of it, talking about the Fermi liquid and the possibility that helium three was a Fermi liquid. Brueckner said, “Could this possibly be one of your aligned angular momentum states on your orbital angular momentum states?” And I said yes and set Pierre Morel, who had come to me as a student, to do a formal theory of it. We looked at the interactions, and the very primitive interaction estimates that we could make at that time suggested it certainly couldn’t 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, “Hey, I have a graduate student on it too and it was my idea and I do think it’s unfair for you to publish it all by yourself.” 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, “No, no, no, no. There’s nothing like that in nuclear physics.” 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 Pierre’s 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 don’t 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 it’s very likely a higher angular momentum state because of the existence of the two phases, the A and B phase. So we discovered the physics behind this multiple phase structure which has, it’s 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 don’t satisfy simple angular momentum group theory because it’s 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 paper. The other was duplicated by a number of other people independently. I don’t 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. You’d 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 didn’t. 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 because of an offer that I had from Stanford and had gotten to know Bill Fairbank who was the tame experimentalist at that conference. Bill Fairbank and Cor Gorter had an interesting conversation when we later visited Gorter where they both talked about their efforts to discover flux quantization. As you know, Fairbank won; Gorter had the wrong idea. Fairbank knew why it was the wrong idea, but he wasn’t about to tell him why it was. He told me later on why it was the wrong idea. Gorter 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 he’s a very straight laced, fundamental Christian. He talked very nicely to the ladies, but we didn’t 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 don’t 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 ab initio. 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 Brueckner’s 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 weren’t 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 didn’t 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 haven’t really done it right, as you know.
So let’s 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 connected?
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.
We’d 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 didn’t 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 Hilbert 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?
‘59. Well, the first time I had been to England since 1937 when I was there as a kid, the first time I’d 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 I’d 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, “Well, I’m interested,” 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. I’d heard about the peculiar teaching systems that these universities have and I said, “Could I give a lecture and would anyone come and listen?” And Roger said, “Oh, no, you don’t need to do that,” the implication of which was very obvious. And Brian said, “Gee, that would be great,” essentially, although Brian never said, “Gee, that would be great.” Brian said, “We would very much enjoy having you do that,” 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 didn’t 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 physics that I didn’t 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 I’d 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, “We have no Dr. Josephson here,” and he kept probing and said, “Oh, him. He’s an undergraduate.” 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 of 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 he’d 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?
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 wasn’t sure. I think he had done it at first the right way, but he wasn’t 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 can’t see anything wrong with it,” and from that point on we discussed this and he came to the tea table often and we discussed it at length. We didn’t really understand totally what the interpretation would be. Now Brian Pippard claims that I was the first one who said, “Oh, I supposed it’s really a current proportional to sine phi.” The expression that Josephson had didn’t make that explicitly clear. So according to Pippard, that as part of my role and part of my role was just to say, “Well I was really persuaded...” talking to the convinced I guess in Josephson’s 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 didn’t have much of a role in what Josephson did, except to say, “Yes, it’s real. It’s fine. And it’s important that it is actually an explicit way of measuring the phase of the order parameter, the important constituent in the order parameter.” He was responsible, for instance, for finding the tiny little bit in Gor’kov’s derivation of Landau Ginzburg that said that the phase varies with exp(imut), in other words, the Josephson relation for the frequency, which Josephson cribbed out of Gor’kov, but it had no prominence in Gor’kov 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, “You have the wrong thickness in your dependence on magnetic field,” 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 Physics Letters and not Phys Rev Letters, and partly also it had to do with that the Cavendish didn’t want to spend money on publication charges. But then he did a full theory complete with the the fact that with the current there was an accompanying energy, 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 didn’t 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 of doing superconducting tunneling experiments, and I said to John, “You must look for a glitch near zero voltage, because there is this term that Josephson has derived and he’s derived it correctly; it’s really there and we don’t see why you don’t see it.” 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, “We found that it’s very sensitive to field,” and I estimated, well, I wrote him the whole story as to what we’d seen and I estimated that its sensitivity to field was a little high because there wasn’t 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 corrected me. 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 Brian’s, 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 couldn’t have seen it. So I now believe that probably we were the very first to see it because of John’s excellent junctions. The main thing I did, well the first thing I did in this letter was to address concerns 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 didn’t have to renormalize all of the quantities, 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 paper. 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 collective mode of the phase. I calculated this, which was not in any of Josephson’s 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 it’s in the paper. My dilemma was that I was aware of the Matthew Effect, not the Peter Principle, but the Matthew Effect: “To him that hath shall be given. From him that hath not shall be taken away even that which he has,” 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 wasn’t that odd. I shouldn’t have worried. Josephson was perfectly capable in this kind of regard of taking care of himself, but I didn’t realize that. He also had a lot of advocates on his side, Pippard and the Cornell group and so on. 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 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 that’s why the main paper is this lectures on the many body problem, edited by Caianello, because I didn’t want to publish Josephson’s scholarship thesis essentially before he did, and he was very firm in feeling that he had published all that and he didn’t 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 didn’t think of. Josephson did later write a review article that had some things that I didn’t think of, so both articles are useful. Then the real review article that I finally wrote was for Gorter’s Progress in Low temperature Physics. That’s 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.
It’s 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 never quantified. 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, Bean’s work, he’d been reproducing Bean’s work and thinking about it. He had a new geometry 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 doesn’t 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, “That’s a logarithm.” I didn’t 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, “Your flux is decaying logarithmically. And the reason it is decaying logarithmically is because the vortices are creeping through the material. The vortices are moving.” 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 ‘64 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 that’s 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 didn’t play with that very much. So all of that followed from thoroughly understanding Josephson and how it worked.
A subsequent topic connected with superconductivity, we’re 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 Pines’ graduate student, but Pines didn’t 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 couldn’t leave New York with him because Pierre was simultaneously the cultural attaché in the French Consulate in New York. He was Nozieres’ 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 I’d been thinking. Well, I’d 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 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 don’t remember exactly when his paper came out; it’s 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 didn’t even remember the Russian’s name. Later on when Pierre went and gave a seminar at Illinois, he dug out the Russian’s name and explained the Eliashberg equations to Pierre, and so Pierre reformulated what we had already been doing, in somewhat more naïve 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 about doing 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 mu- star, an effective potential for taking in account the modification of the isotope effect. That’s 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.
‘62, I’ve got.
It was published in ‘62 but done in ‘61. I talked about this actually in Birmingham with Rudolph Peierls in the audience, and Rudolph Peierls said, “Gee, that’s interesting. Isn’t there some way that one might observe the fluctuations in the order parameter that you’re predicting,” 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 don’t 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, “Well, Prof. Peierls, you’re absolutely right, there should be some way to measure this.” Two weeks later I received a phone call from John Rowell who had already started doing his tunneling work in which he said we’re seeing bumps on the tunneling spectra of superconductors, of tunneling between superconductors. And he published a paper. Jim Phillips, as is his custom, jumped in on the theoretical side of that paper and said, “Hey, the two bumps there, look, you’ve got harmonics of the phonon spectrum.” There’s one at one, and one at two, and he invented one at three. But at far as I know, Phillips’ 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 wasn’t Morel but probably Chynoweth who talked to me, and I said, “But we’ve actually calculated that kind of thing in this paper with Morel,” 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 let’s 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 Doug Scalapino with him, and they said fine, we’ll 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 Eliashberg’s 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 ‘87, 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.
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 on to Bill McMillan, who had just come into the department as a post-doc, and Bill being a very stubborn and very brilliant guy, said, “We don’t need to postulate spectra and calculate the characteristics. Let’s take the characteristic and calculate the spectrum.” And I said, “But that involves inverting this very, very messy, integro-differential equation.” And he said, “I can do that.” 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 transforms, and he looked at me and said, “I don’t need that. I’ll do it my way.” And this was very characteristic of Bill McMillan he did things his way. He said it very slowly, “I’ll do it my way,” [stuttering], but you couldn’t change his mind. But it was ten years later, he said, “It really would have been easier your way.” 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 didn’t 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 I’d 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? (biographical note — it was the second trip to England that year 1959)
Well that’s 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 ‘59 Cambridge meeting and they also visited Harwell.
May I just ask, how did you resolve the bet with the sign?
I don’t remember. It was eventually possible to experimentally discover the sign. I think it was a matter of, I don’t remember. But it’s a considerably subtler effect to discover the sign.
It was through the Mossbauer measurement?
Yes. I don’t 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 doing a study 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 to Friedel. 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-Gor’kov theory of magnetic impurities and superconductivity, and I’ve always regretted that because I was quite wrong; their theory was right and Harry Suhl’s 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 don’t 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, “Look, if I put iron in such and such a compound, if I mix iron and rhodium, or a compound of iron and rhodium, this compound isn’t bothered at all. The iron electrons join the D band and become superconducting.” 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 impurity. I realized there is this crazy dichotomy between cases in which the magnetic impurity was magnetic and cases where it wasn’t. 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 wasn’t some delicate experimental fact like the Knight shift, or like the Lamb shift, that you had to go to extreme effort to discover. This really stuck out like a sore thumb, this dichotomy. So I said, “There has to be a theory for a dichotomy. It’s simple enough, simple as that.” So I started from this idea that I’d borrowed from Blandin and Friedel at the Brasenose College discussion, and my parameter U, which they hadn’t had, and I said, “Let’s do a resonant state with the parameter U, and that’s the localized magnetic model,” 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 didn’t 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 couldn’t 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-Stratonovic and that kind of structure. I think I was quite wrong to be a little annoyed that he didn’t 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 didn’t 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 Piers 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 ‘59 and in June ‘59 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 Friedel’s virtual state idea for impurities in metals, and I gave a talk there. Here it is, “Discussion Brasenose College, Oxford, England: New Concepts in the Magnetic Transition Metals.” 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: “Anti-ferromagnetic Contribution to the Polarization of Free Electrons by Inner Shell Spins.” 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 there’s 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 didn’t 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 that’s 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, that’s it’s totally localized and it’s 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 ‘64, “Localized Magnetic States in Metals.” 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 they 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 ‘65, if I’m not mistaken.
Was it really that late?
If I’m 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 ‘61 or so?
Already in ‘61, essentially as a response to my paper. He said, “But you can also do it with the states from the band itself,” a localized U rather than a localized orbital.
So by the time you’d reached ‘64, the equivalence between the two was known?
That’s why it’s 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 ‘61 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 ‘61 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 crossover. How did that happen?
Well, I think the first hint was really Bob’s talk about the Schrieffer-Wolff Model, and he said something that amounted to the 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 assumption of a spin one-half, so you’re 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. That’s talked about at least in this paper. 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 didn’t 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, a kind of I would say rather ad hoc generalization of dispersion theory that sounded very fancy mathematically, but it wasn’t 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 we’re 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 you’d gotten to that, you’d 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 Kondo Model. It just didn’t 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 ‘66 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 don’t really know why they didn’t quite get the answer right, but they never did and they used Hubbard Stratonovich and it didn’t seem to come out right and the answers were ambiguous and I’m 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 formalism, but they weren’t using spin rotation invariant boundary conditions. They weren’t using cutoffs that were spin rotation invariant, and so they got into a totally terribly wrong answer because they lost spin rotation invariance on their cutoffs. I think that would have been an equally easy mistake to make in the Hubbard Stratonovich group.
This is a bosonization approach to the problem?
Well, no, but in 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 that’s wrong about that and something that’s 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 you’re 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 Green’s functions using outgoing boundary conditions which were completely independent of what happened at infinity, and I found a way to derive Fermi’s or Friedel’s 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 didn’t publish it or it isn’t 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 wasn’t 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 — >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 didn’t 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 it’s called.
CPA. Bill, and his young post-doc, are co-inventors of that with the guy at Penn who is normally credited with CPA. [???] said, “I can’t see anything wrong with it,” and from that — 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. It’s an effective medium theory or CPA or whatever you want to call it. But it’s very nice and I tried to use this for transition metals, and it would have been just fine except for this horrible mistake in the middle, which a student named Olsen of Walter Kohn took as his thesis topic. Walter told him, “Heavens, you mustn’t publish this. You are saying that Phil Anderson is wrong.” 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 Walter’s behavior to him because he was absolutely right. He was absolutely right all along. That was not the formal theory of resonances, but I haven’t 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 Green’s 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, “I think there’s a logarithmic divergence here.” And again Walter Kohn is the villain you know, he’s such a nice man, everyone thinks he’s wonderful, but he’s the villain of this. He had written a paper with Majumdar, which was already in the literature and we’d 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 at 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 there’d 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 k’s near the Fermi surface, there was no singularity whatsoever at that point. Which is right. Of course there’s no singularity whatsoever.
[in the occupation].
The occupation n(k) or any other. He calculated n(k) and he even said, “Well, it’s probably true even for interacting electrons in Fermi liquid theory.” 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 didn’t understand that that’s what he was doing because he had so much perturbation theory and before he ever got to the question of calculating the Green’s function he thought of the Green’s 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 didn’t realize there was a general theorem here. He did extrapolate. He did say, “This is probably logarithmic,” and he had more or less the idea where the logarithm came from. So it’s 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, “You 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,” and he thought it was a little unfair. And I said, “Of course it’s unfair and I wish I’d put your name on it,” but by that time all the papers were published. But then you’ll find in the eventual work on the Kondo problem you’ll find effusive acknowledgements of John’s 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 school. In the course of doing that, let’s see, what had happened? The first thing that happened was I was really stupid. I could get the infrared catastrophe at T=0, and I didn’t 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, couldn’t 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, “But you can do it on the back of an envelope,” 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 deDominicis’ idea, and you immediately get the power law propagator. And Yuval was already my student and when I explained this to him he said, “You idiot, of course this is true.” (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 it’s 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)+ deltakAnyhow, it ends up that you have a Cauchy determinant of one plus phase shift and this Cauchy 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-deDominicis’ 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-deDominicis’. What is an even better way is probably Bosonization. I don’t know, but we hadn’t yet thought about bosonization.
So that was in the ‘69 paper?
This is in the Localized Moments, this is on page nine. I give the determinantal technique in the lectures.
And you’ve already started working with Yuval by that stage.
Yes. Okay, let’s go back. Life. Nottingham. Then that was the summer of ‘64. The years ‘65, ‘66 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 I’m still not convinced that we hadn’t 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 don’t 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. It’s 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 couldn’t 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 classical fluid.
Definitely you want to link this up with Yuval.
No, no, this is totally different. I decided we’d better go back and clean up all these things. I’m 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. You’ll also find a good paper by Volker Heine. By now I’d 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 won’t 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 wasn’t 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 wasn’t 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 hadn’t been formally announced yet. The electors had met and suppressed the chair and replaced it with a visiting chair and all that, but it hadn’t 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 he’d 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 wouldn’t want to go,” and I said, “No, absolutely not,” and started suggesting names. "Under what conditions would you go?” he said. And I said, “If I could stay at Bell half time.” I was tired of turning down offers from various places. I’d turned down a suggestion, well, 1960 I turned down Stanford which is the only one I ever really came close to regretting. But I’d turned down various other places and Joyce said to me, “If we are not going to take this one, we’ll never do anything adventurous.” And so we decided it would be an adventure and we’d 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 Christiane Caroli whom I’d met at the ‘63 meeting in Ravello and become very fond of, both Carolis. 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 Regent’s lecture, and that was the occasion in the spring of 1967 when I gave the Regents’ lecture. Joyce had flown to England because our real estate agent said there’s an auction of a house and we think you’d 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. Mary’s 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 Holden’s who was working at the same private school where he was, but what Steven hadn’t 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 didn’t 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, “You’d better let that plane come. It’s unconscionable.” I don’t 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. He’s 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 wasn’t necessarily. But we had a good time with Bernd and we would go to this Mexican joint with him and Joan 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 that’s where “More is Different” came from, that was the Regents lectureship. So then I went to England and we thought we had the house signed and sealed. Well, you know, in America real estate deals are you shake on it and it’s done. We didn’t know about gazumping, but somebody gazumped us out of our house on Little St. Mary’s Lane and we ended up in the coldest flat owned by the University of Cambridge and that’s 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 for me, he got the ragtag and bobtail (he got Basques, he got Turks, he got Israelis, he had an Ibo among others, and I don’t 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 Bullett was a Northern Irishman. But miscellaneous students and some of them were good and some of them not so great. 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 ‘68, and thought very hard about it and came back with the sum over spin flip paths, and I said, “This spin flip path with Muskhelishvili equation tells us that this thing is really a classical gas of spin flips, and that’s what we have to solve.” So that’s the basic paper. 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 ‘70 is that it was stopped by the referees in Phys. Rev. (Phys. Rev., not Phys. Rev. Letters, we weren’t even trying to get something into Phys. Rev. Letters.) The referee, Bob Schrieffer had admitted, was him. He said he didn’t believe it; 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 Gor’kov and Dzialoshinskii had been sprung. Gor’kov 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 ‘69, and I didn’t 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 block method in RG theory 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 it’s 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, there’s a factor of two between each of these which were factors of two that Wilson didn’t find exactly, we found them exactly.) So I’ve always contended that our method was better than Wilson’s. It subsumed Wilson’s 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 it’s 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 an unsolved statistical system, and we pointed out that we had also solved the statistical system in J. Phys. C.
There’s ‘70 and there’s ‘71. Both have this discussion. What page is that ‘71 in?
‘71 is page 11 near the bottom.
Oh, yes, that’s it. That’s 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 mathematicians’ point of view, it’s 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 hadn’t solved that. He said it involved logarithms and he didn’t know how to sum the logarithms. We did. So we did sum the logarithms.
What happened to Yuval actually?
He’s now working for Microsoft. He’s working for Jennifer Chayes. He spent a long time in Israeli intelligence and then he came and worked for Microsoft. Worked directly for Norvald, the Princetonian who’s in Microsoft.
He was at Microsoft.
Yes. He was at Microsoft and then transferred into Jennifer Chayes’ group. I don’t know what he does for them. Jennifer told me that he still expects her to write down the results that he finds. He hasn’t 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 don’t remember exactly. It was fairly important, but it was not — What Gideon and I had done is already essentially there in that first paper.
Don was a post-doc at Bell at that point?
No, I think maybe he’d 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 didn’t 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 there’s 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. There’s 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 don’t really like about that because that doesn’t 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 Toulouse 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 it’s 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 wasn’t 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 Thouless 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, it’s 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 don’t we move onto some work on spin glasses and then perhaps we’ll 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 there’s a paper with Harry Suhl) about superconductivity. I don’t know where that appears. We were worrying about these results.
‘59, Spin Alignment in the Superconductive State.
‘59. 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 there’s 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 wasn’t necessarily ferromagnetic anyhow. Bernd called it a ferromagnetic transition but it wasn’t, but we didn’t 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 didn’t 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 ‘67, ‘68, something like that. All this time I was saying to Bernd, “That isn’t a ferromagnetic transition; it’s something messier, and we don’t know what really is going to happen there.” And this funny little graduate student, Wai-Chau Kok, 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 didn’t speak perfectly good English, she was from Singapore, but because she squeaked.
So she didn’t overlap with Yuval, I gather?
Yes, she overlapped with Yuval.
The paper from ‘71 on page 12. Comments on the Ferromagnetic Theory Consisting of [???] Magnetic Alloys.
Yes, I think there’s an earlier one. Oh no. There’s 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, it’s 1/r3interaction. 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 Kip’s 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 didn’t know about the Kondo problem and part of our bewilderment was we didn’t 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 polarizes the lattice, but then there was this concentration problem. So I said, “Well, the manganese spins, you can linearlize the problem, and then you have, if it’s a quadratic exchange interaction you can find the eigenfunctions and eigenvalues of that exchange interaction and there will be some first extended eigenvalue of the exchange interaction and then you should have some kind of freezing into a disordered magnetic state.” And I think that’s 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/Χ 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 that’s what I set Wai-Chao Kok, 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 that’s the one where we showed that in a crystalline structure you would get a finite theta and in an amorphous structure you wouldn’t. 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 I’ve 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 couldn’t have any localized states. The localized states would be killed by the non-linear terms in the interaction essentially by the fact that it’s a sigma model that the spin can only get so big, so that any local eigen function would displace, 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 Bernd’s, 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, it’ll be clear that I was puzzled about why there wasn’t a phase transition, actually. So all this time we were going on under the mistaken assumption that there was no phase transition, so we didn’t 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 didn’t read that Wheatley paper. I guess I was so miserable about the journal and I didn’t like to read things, I blanked it out.
So then when Canella 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 didn’t look back at John Wheatley’s data and say, “Well, he’s obviously right because look at John Wheatley’s data.” The difference between Mydosh and Wheatley is just this. Mydosh was a peak and Wheatley was the field cooled case because he couldn’t use a big field, he had to cool it in the Earth’s 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 extract the...
Yes, that was a high temperature. That was strictly high temperature. I didn’t want her to get messed up with this real mess. She’s still in physics. She’s 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 she’s fairly happy there.
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 let’s get to that later. The first amorphous magnetism conference, Hooper and the notorious DeGraff editors. DeGraff is one of the stupidest men I’ve ever had to deal with, and for a long time he ran all funding from NSF for material science, and that’s 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 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-Chao’s thesis and a couple of other ideas I had. But I just didn’t say out loud, which I should have, I’m surprised there isn’t a phase transition. But you realize that this original paper, spin glasses, if its implications were followed out, would have said there was a phase transition. But this continued to be puzzling. Now where do we get back to? We don’t 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 Mott’s retirement. No, it wasn’t Mott’s 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 I’ve never forgiven him. He hired a man named Cook. Cook was a man whose contributions could not be found in the 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, “I’m never going to darken your door again,” except I was about to do that anyhow. I didn’t. I didn’t 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. I’m not sure we shouldn’t have done that, I don’t know. Michael hadn’t 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 can’t 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 Pippard’s professorship, I think. I don’t know whether it was Pippard’s or Frisch’s. It was one of the old, established professorships. But Edwards 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 didn’t apply for that job, but did get a professorship when I left. That may even have been fixed up, I’m not sure. Anyhow. Sam and I talked about glasses and spin glasses and so on, and Mydoshes’ results were just out. I said, “Look, we’ve got some data now. There is a phase transition.” 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 didn’t seem to work. Said, “Well, maybe this will work.” 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, what we would now call random landscapes on the board and said, “The essence is you’ve got this random landscape and how does the system respond to it?” And I got this argument that it should find an extended state and freeze, so I’m happy that there’s 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 it’s a Q-squared over T-squared instead of a Q over T that comes in. Otherwise it’s the same thing. And that was it. We published it before he ever arrived in Cambridge. I had been quite unhappy with Pippard’s being chosen as the Cavendish professor. He’s such a pessimist. He had this English attitude. I guess it’s conditioned by wartime or something, that if things are going to be bad, let’s accept it and let’s really make the best of it rather than things are going to be bad, that means you’ve got to fight to improve them. And he said, “Okay, our students are not being used by UK industry. The good ones are going overseas. So let’s train them for UK industry instead of training UK industry to use our students, let’s train the students for UK industry.” 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 I’d go back home and John Hopfield seemed eager to see if he couldn’t 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. It’s 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 = 0 trick. And deGennes has an n = 0 trick that’s based on that rather than the other, leaving the loops out of diagrams. But Sam’s 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 doesn’t require replicas at all. It says, Let’s do it once and then do it twice and see if there’s a correlation in the background in the mean field, how much correlation can that induce in the local spin?” So in a sense it’s that. But it’s not motivated really by the interaction trick. That seemed to just not work well. There’s 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 didn’t 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 I’d 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 didn’t really like it. I knew that existed, but I didn’t work in that direction very much.
This is a good place to stop.
Well thank you. We learned a lot.