Bertrand Halperin

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ORAL HISTORIES

Credit: Paul Horowitz

Interviewed by
David Zierler
Interview date
Location
Video conference
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In footnotes or endnotes please cite AIP interviews like this:

Interview of Bertrand Halperin by David Zierler on April 21, 2020,Niels Bohr Library & Archives, American Institute of Physics,College Park, MD USA,www.aip.org/history-programs/niels-bohr-library/oral-histories/44555

For multiple citations, "AIP" is the preferred abbreviation for the location.

In this interview, David Zierler, Oral Historian for AIP, interviews Bertrand Halperin, Hollis Professor of Mathematicks and Natural Philosophy, Emeritus, at Harvard. Halerpin recounts his upbringing and education in Brooklyn, and his decision to study at Harvard as an undergraduate. He describes some of the leading physicists of the department during that time, and his developing interest and talent for theory. Halperin describes a formative summer internship at New York Life Insurance Company and his work at the dawn of the computer age, and another summer internship at Los Alamos, where he worked on a project on neutron scattering from aluminum. He explains his decision to move to Berkeley and then Princeton for graduate school where he developed his interest in solid state physics. Halperin describes his post-doctoral work in France and his subsequent job at Bell Labs, where he worked on dynamic critical phenomena. He describes being recruited back to Harvard by Paul Martin and his subsequent work on quantum Hall effects and one-dimensional systems research. In the last exchange of the interview, Halperin describes his current interests in experimental puzzles and the behavior of quantum systems.

Transcript

Zierler:

Okay. This is David Zierler, oral historian for the American Institute of Physics. It is April 21st, 2020. And it is my great pleasure to be here with Dr. Bert Halperin. Dr. Halperin, thank you so much for being with me today.

Halperin:

Well, it's my pleasure. Thank you for being willing to interview me.

Zierler:

Wonderful. All right, so let's start at the present with your title and your institutional affiliation.

Halperin:

My affiliation is Harvard University, and my title is Hollis Professor of Mathematicks (spelled with a C-K) and Natural Philosophy, Emeritus. Emeritus means I'm not teaching anymore. I don't have post docs that I'm responsible for. I work with other peoples' students. I like to speak with students. And I try to give them advice. Until the coronavirus, I would often meet with post docs from the theory group and enjoy interacting with them. But I'm not supervising them. I guess, in a way, I've been working more with experimental students, because I've been working quite a lot recently with two experimental colleagues, Amir Yacoby and Phillip Kim, often getting interested in their research projects, and I'd be with them and their students and post docs in connection with those projects. And then there are other people who come to speak with me, including students and post docs, whom I enjoy interacting with, but I'm not responsible for finding them problems or supervising them. I would also say that I don't have responsibility for their future careers, except that I do, obviously, have to write lots of letters of recommendations (laughs) for people: Present students, former students, et cetera.

Zierler:

So the title is interesting, because you're in the department of physics, and yet the title is professor of mathematicks?

Halperin:

Yeah, well, okay, so before I retired, I was the Hollis Professor of Mathematicks and Natural Philosophy. This is actually the oldest chair at Harvard, other than the Hollis Professor of Divinity, it's probably the oldest chair in North America, certainly in Natural Sciences. It dates back to 1727, and in those days there was not really a separate discipline so much of physics, natural philosophy, and mathematics, where it was sort of lumped together. And of course, you know, people like Newton were... Newton, which wasn't that much earlier actually. Newton was only 40 years earlier. 50 years earlier. They did mathematics and physics, but also other aspects of natural sciences were sort of all linked in that title, and the Harvard College, at that time, recognized that its goal was not only to prepare ministers and not only teach them theology, although that was the most important thing, but they should also have knowledge of the sciences, and the languages, of course, and so this, that's where the title comes from. And it's spelled with a "C-K", "mathematicks" with a C-K, because that's the way it was spelled at that time. And it's very hard to keep that "K", especially in the days of autocorrect.

Zierler:

Right. (laughs)

Halperin:

But for generations, we have fought to keep it. My predecessor fought to keep it, and I also. They tried to take it away from me when I was made, when I got the title, but I fought to keep it. In my case, I thought it was important to keep the K because, although I'm sort of, I guess, knowledgeable about 18th century mathematics, I certainly am not knowledgeable about 20th century mathematics, or even 19th century, all of that, and I'm sure that the math department is happy that I'm not considered a professor of mathematics without the K. (both laugh) So that's--

Zierler:

That's funny.

Halperin:

That's the story.

Zierler:

Okay, so let's go right back to the beginning. Tell us about your birthplace and your early childhood.

Halperin:

Okay, well, I was born in Brooklyn in 1941, the day before Pearl Harbor, actually. And so it was quite a shock to my mother when she had this one-day-old baby boy and she was afraid I'd be drafted. And but I have really no memories of the war.

My father was a civil servant. He worked for customs. He was an examiner, a customs examiner, working in, you know, not on the docks, but he examined watches and other imported merchandise. So he was a civil servant. But he was an amateur mathematician. He had been very interested in mathematics and had had ambitions to actually become a mathematician, a mathematics professor. He had a masters of mathematics. He had written a couple of papers. I think, he went to City College as an undergraduate, then he went to Columbia Teacher's College, I think it was where he got his masters degree and wrote several papers, and he would have liked to have gone on to do a PhD, but it was the Depression. He had a government job. He really had to support his parents, and his sister, and he actually applied... It's quite interesting, something I found out much later, is that he applied to Harvard, maybe other places as well, for graduate school. And he was admitted, as a graduate student, but they said they couldn't give him a fellowship. So he couldn't go, and that was the end of his professional math career. But he always enjoyed doing mathematics. It was a sort of a hobby for him, and he loved to solve puzzles. He loved to teach, in fact, as a tutor to various... When kids in the neighborhood or building had problems, they would come to him, or relatives, or friends or children of friends. And he always liked that. And certainly that inspired me. He never pushed me in any way, and never prodded me, but I think I enjoyed math as a result. You know, I saw him solving math problems and he certainly encouraged me. So that was an aspect of my life. And he was always interested in science.

Zierler:

Were your parents native New Yorkers?

Halperin:

No, no. Both my parents were born in the Ukraine, in what's now the Ukraine. It was then part of Russia. My father was born in 1911, and his family... 1907, sorry, and my mother was born in 1911. Both of them came to the US as children. My father came with his mother, his family, in 1914, just before World War I. And my mother was born in 1911, and she, her family didn't get out until 1919, 1920, so she was in Russia through the war, and suffered and all that, but she never talked about it. She didn't like to talk about it. Didn't remember. When she came here, she was about 9, and she basically claimed she didn't remember almost anything from before that time. But she had older sisters, who were much older, who remembered a lot. So, I knew something about it. That was the background, and they met in Brooklyn. My mother went to Brooklyn College. She actually majored in mathematics but never went on in it.

Zierler:

Oh wow.

Halperin:

She became, at one point, I think she was an elementary school teacher. Then at some point, she met my father in the 1930s and they married. When I was very young, she was just a home maker, but when I was about ten years old, she took a job. She worked in the registrar's office at Brooklyn College, again as a kind of administrator. Relatively low-level, medium-level administrator.

Zierler:

And for primary school, did you go to public school or private school?

Halperin:

I went to public schools. When I started out, I went to the neighborhood public school, which had the name of PS91. I went to PS91 through the fourth grade and the beginning of the fifth grade. And I was reasonably happy, and but at the beginning of the fifth grade, they decided to abandon what we would now call "tracked" learning, I think. By third or fourth grade, we were already sort of tracked, and the kids were somewhat selected. By fifth grade, I was put in a class which, you know, had three reading groups, three math groups, three everything. And there were pretty much the same kids in each group. And the teacher, of course, had to spend most of her time with the lower group, with the middle group and the lower group, and so we had a lot of busy work and a lot of writing and I hated it. My parents then took me out of that and sent me to what we now call a magnet school, which was called PS208. And that was something where I had to travel to. It took me, you know, maybe half an hour to get there, 45 minutes, by taking two-- I basically took two buses and a subway, which at that time, you know, was considered acceptable. It was okay, you know, I was in fifth grade.

Zierler:

Sure.

Halperin:

They were sure I could travel by myself. In fact, even when I was eight, I was taking music lessons in Manhattan, and I used to go to Manhattan by the subway by myself when I was eight. Now, you'd get arrested if you let your kids do that. But anyway, PS 208 was very nice. The school had a couple of special enrichment classes, where the kids were selected. They came from a large area of Brooklyn. There wasn't an exam to get into the school, but I think you had to maybe do an interview with the principal. And she was a very capable leader. And so we learned. They taught us a little bit of French, and we learned typing and we had relatively advanced projects. Now that was quite a stimulus. So that was the selected school. And then in junior high school, New York City at the time had, (I don't know if they still do), they had these special progress classes where you could do seventh, eighth, and ninth grade in two years. You had to take an exam to get into that, and I think around 15% of the kids went through this. It was somewhat elite. And again, that was stimulating, and I had very good teachers. I had some good teachers there who encouraged me to go ahead by myself in math, and science, so I studied. My math teacher said I didn't really have to take the algebra course; I could go ahead and study geometry on my own. And I... I had a very good French teacher who was kind of inspiring, and I actually came in second in the City in some kind of a French contest. Language is not my greatest skill at the present time, but okay, at the time I guess I had some talent for it, and I was interested in it.

And then I went to high school. I went to something called George Wingate High School, which was just the local high school. I had taken the exam for Stuyvesant, and a lot of my friends went to Stuyvesant, but in the end, I decided I did not want to go to Stuyvesant. It was actually a difficult decision, I went back and forth a couple of times. I didn't really want to have to commute 45 minutes each way every day, or an hour each way, and I didn't really want go to an all-boys school, which is what that was. I didn't think that was a good idea socially or in other ways. Wingate was, of course, an ordinary co-ed high school. That was an influence in me.

Zierler:

Would that have eliminated Brooklyn Tech also?

Halperin:

Yes, it would have. But at that time, Brooklyn Tech was not an attractive option. Brooklyn Tech had been one of the really leading schools, but by the time I was choosing a high school, this was 1955. At that time, Brooklyn Tech was not considered nearly as good as Stuyvesant or Bronx High School of Science. Bronx High School of Science might have been the best. It was also co-ed. But that would have been an hour and a half each way. That was not practical. And Brooklyn Tech was not particularly attractive. Also, it was a huge school; it had 6,000 students.

Zierler:

Did you get a strong education in math and science in high school?

Halperin:

Yes, yes, I did. Partly because I taught myself, and the teachers encouraged me to do so. For example, I studied advanced chemistry, and they let me do lab experiments by myself. I did college level work sort of largely on my own. I had a good biology teacher, and I had a very good physics teacher, but I was a little advanced for the classes, so I can't say that I learned that much from them. But they encouraged me, and my biology teacher encouraged me and a friend of mine to do some work by ourselves. We did some experiments with rats, which would have been impossible nowadays. No way would it be allowed. We had a colony of rats, and we were doing experiments with them.

And there was a math team, which competed around the city, and that was important for me. I was sort of the leader of the math team. And that took a lot of effort and, you know, I studied and I worked on it. There was a teacher who supervised the math team, and he certainly encouraged us. I can't say that I remember learning a lot from him especially, but he encouraged us to study for it, to work on it. And I had several friends in the math team, who were close friends, who were also active in it. Plus, several of my friends, one of my closest friends from junior high school, who did go to Stuyvesant, was also very good in math, and he was on the Stuyvesant math team. So there was a competition between us, and there were some other kids in the neighborhood who went to Stuyvesant who were involved in the math team. So, it had a social as well as an intellectual aspect, and I think that probably was important in the development of my interests in math and science.

Zierler:

What year did you graduate high school?

Halperin:

'58, 1958.

Zierler:

Okay. And in choosing—

Halperin:

Which was the second graduating class of Wingate High School, it was a new high school at the time.

Zierler:

Okay, oh wow. Okay. And in choosing college, was Harvard always the dream, or did you apply to a lot of top schools?

Halperin:

I applied to five schools. Harvard, I guess, was my first choice from the beginning, but I didn't know how realistic that would be. There were also financial issues. I applied to Columbia, I applied to Cornell. I think I applied to University of Pennsylvania, maybe, and also maybe Amherst. I can't remember. I applied to five schools. Which was maybe a lot at the time. I gather, students apply to far more of them now. But I didn't know that I'd get into any of them. Well, I knew I could always go to Brooklyn College if I didn't get in to one of the private schools, and I think I considered Penn was pretty much a sure thing, but I wasn't all that confident of getting into any of the others at the beginning.

Zierler:

Were you a strong student across the board—?

Halperin:

Yes.

Zierler:

Or did you really distinguish yourself in math and science?

Halperin:

No, I was strong across the board in... I was not the top student in my class. I was second. There was a girl who had higher grades and a grade point average. So I was strong across the board but you know, that in itself… You could be valedictorian and still not get into Harvard. Certainly, now, it barely gets you anywhere. In those days, it was less competitive. But the fact that I was first in the city in some of these math contests, (sometimes I was first, sometimes I wasn't) that gave me some degree of confidence; but even so, I wasn't sure. And then there was a state scholarship-- I wound up being, I think, first in the state in the New York State Math and Science scholarship exam. There was a sort of a Regents exam that they gave for that. And there was also a general exam. I was, I think second in the state i that overall. So that was something that might have given me confidence that I would get in, but those results didn't come till, like, May. I think I was already into Harvard. I was also a finalist in the Westinghouse competition. There were 40 of them in the country, I don't know if that would have by itself have done that much for me, but there was enough going for me that I probably should have been fairly confident about getting into Harvard, but I was not particularly.

Zierler:

And coming from-- I don't know how well-traveled you were, you know, beforehand, but what were your impressions when you got to Harvard? Did it feel like a different world, or was it a pretty natural transition for you?

Halperin:

Okay, so first of all, with "traveled": I don't think I'd ever been as far as Boston. I had been to Atlantic City once with my parents. I think that was the furthest I'd ever been from home. I'd been to summer camps, so I'd been away from home. They were in the Catskills, and they were more like home in a way. But I don't remember ever feeling like a fish out of water or anything. There were a lot of other, or a reasonable number of other kids, who were Jewish kids from New York, and who had been in math teams and stuff that I knew there or I met there, and they had similar backgrounds. But then there was, in my freshman dormitory, in one of the next rooms, there was a fellow from Oregon that I became pretty close with, who was from a relatively rural area. Not from a farm, but he said he had never met a Jew in his life before he met me. He was pleased to see I didn't have horns, I guess. And he was not a mathematician. He's still a friend, David Mack. He eventually went into the Foreign Service. He studied Arabic and was stationed throughout the Middle East. He eventually became an ambassador to the United Arab Emirates, and was high up in the State Department, and maybe head of the Middle East desk and so forth. So his interests were very different than mine, but we were close, that was certainly a change for me. But I didn't feel, I wasn't intimidated by the place. You know, I felt I could hold my own among these other kids. At least, I could in science. And so...

Zierler:

And did you know entering that you were gonna major in physics, or did that decision come later?

Halperin:

No, no. Well, there were three-- So when I entered college, I really was not sure whether I would go into medicine or physics. Those were the two main choices, and I also considered, as a fallback, actuarial work, that's for life insurance. I'll fill in on that in a moment, but basically, I was always very interested in math. My route had been to physics was largely through math. I was someone who loved to solve math problems. I was certainly interested in science. I read all the science books I could and stuff. But I wasn't an experimenter particularly-- I mean, I had a chemistry set and I did do a few scientific experiments, like to make some explosions and stuff like that. And my friend and I had some science fair projects. But I wasn't a real tinkerer… I was interested in math, but I was more interested in applied math, I guess, than really pure math. And I didn't really think I was good enough to do real abstract math. I thought maybe I should do something more applied, like physics, and I thought that in physics, if I wasn't good enough to be a professor, I could probably get, you know, some employment. All while the logic may not have been particularly good, those were factors. And the idea of applying math to problems in the real world certainly did appeal to me, so that was one thing.

But I was also interested in medicine. Partly, I had a cousin, a first cousin, who was maybe ten years older than me, who was a physician and was pretty inspiring to me, and I was motivated by him. My parents certainly thought of medicine as a good profession obviously.

Zierler:

Of course.

Halperin:

And it certainly seemed like a noble and interesting profession. And I was considering that, but my freshman year in college, I took physics and I liked the physics, and I did well in the physics, and I took organic chemistry. (I was able to skip introductory chemistry because I came in, I had passed the advanced placement exam.) And I didn't really enjoy the advanced chemistry labs so much, particularly, I found the lab hard, and the chemistry involved a lot of memorization, and I wasn't that crazy about that. The labs I found difficult, and well the truth is, in the spring we had to do those, we had to do four hours of lab a week, two hours each of two afternoons. And you had to make these chemicals, you had to make organic chemicals one way or another, and you had to make little quantities. You had to do these melting point tests of them. You have to put a little bit of it in a tiny tube and you have to put it in an oil bath, and you have a tiny Bunsen burner under the oil bath, and you have to raise the temperature less than one degree Centigrade a minute and see where it melts, and you record that. And it has to melt sharply, if it's a pure. If it's not pure, it won't melt cleanly. And then you report this and then you give the sample to the laboratory assistant to make random tests to see if you're being honest. And that was pretty tedious, and you had to have the windows closed because the slightest breeze would blow out the Bunsen burner. And it smelled bad and it was, you know, it wasn't very pleasant, and you could look out the window and it was spring, and there were these young women in their beautiful dresses-- beautiful young women in their spring dresses walking by, and I was trapped. It was sunny outside. And I said, "I'll never make it through medical school if I have to do this." (both laugh) So regardless of whether I might want to be a doctor or not, I’d better go into physics. Not a very good reasoning, not the best reasoning in the world, but that was the way I did it.

Zierler:

Did you have a sense as an undergraduate, but really as a freshman, you know, the giants of the field in the physics faculty there, did you have a sense of who these people were, or that appreciation only came later? The connection went out for a s-- I didn't get. So I don't know if you heard my-- We cut out. My question was on your appreciation of some of the faculty members in the physics department.

Halperin:

At Harvard?

Zierler:

Right.

Halperin:

Mmm...

Zierler:

Like as a freshman, did you recognize what their stature was in the field, or you weren't thinking like that?

Halperin:

Oh, of course, I knew that Harvard was a great place, and I took it for granted that Harvard had some of the best people, but the relative rankings of them, I don't know that I appreciated. So, maybe, the greatest light at the time who was there was Schwinger, but I didn't take any courses from him-- I never met Schwinger when I was there then. Van Vleck was there, but I don't think I really had any contacts with him. Let's see... Well, there were… Certainly, Bainbridge was a leading light, and I later took a lab course from him. But mostly the faculty I found most inspiring were younger people who were not so well known. I’m trying to think. I did have, a course from Norman Ramsey. Actually, that was in my third year, in quantum mechanics, I thought he taught a great course, and I found it very inspiring. Did I appreciate what a great physicist he was? No. I don't think so. I knew he was a great teacher. Did I understand that he was also going to win a Nobel prize? No, I certainly didn't. And Purcell was there, but I didn't have a course with Purcell. I audited a course from Roy Glauber eventually. But I actually didn't appreciate how great a scientist he was. And the course wasn't that much to my liking. In any case, I would say that the stature of individual faculty members was not a big factor for me. Although, certainly, you know, they were doing great work, but as an undergraduate, I was, learning about basic physics and learning about things like electricity and magnetism and quantum mechanics and so forth, that were not at the forefronts at that point. It was the beauty of these basic ideas, and not so much the most current developments, that inspired me at the beginning.

Zierler:

What was your sense of the hierarchy between theoretical and experimental physics, among the kinds of courses that were taught and who taught them and what was emphasized?

Halperin:

Well, of course, I was interested in theory myself at this point. I didn't feel that I had any great aptitude for experiment. I certainly didn't have enough appreciation, by any means, of how wonderful experiment could be, and how much intelligence it takes. I mean, Ramsey was an experimentalist, obviously. He was obviously very bright, and the course he taught was wonderful, but I don't think I connected it with his experimental work. I don’t think I was aware of any kind of pecking order in general. I was only aware of what my own interests were. I was maybe just too out of it to think about departmental politics or things like that. I didn't have any idea what was going on in the departmental politics at that stage. I was too much out of it.

Zierler:

Did you pursue summer internships at all?

Halperin:

Yes, yes. Okay, summer internships, I have to mention that. In spring of '58, '59, and '60, I worked as an intern at New York Life Insurance Company. In 1958, it was the summer between high school and college. I had interviewed for the job, but they weren't really very much interested. They didn't normally take high school students at the time, and they were going to write me off, I think, and not offer me a job. But then, as I said, I came in second in the state, in the state scholarship, and my picture was in the paper and, next day, I got a call from the head of the actuarial department there, saying that they wanted to offer me a position. And then I went back for two more years. The work there was interesting, and in retrospect, influential in my career. I was sufficiently interested in it after the first year that, as I said, I considered actuarial work as a fallback thing for me to do. Actuaries have mathematical responsibilities, but also there's some legal things they have to know: laws and rules about insurance and maintaining balances, etc. But I found the mathematical aspects of actuarial work pretty interesting at the time. I had graduated high school, and I had sort of one year of college algebra and stuff under my belt. So much of the math was new to me. it involved compound interest and probability and various ways of looking at them, of making predictions, and some of it involved symbolic mathematics, like finite differences. I got an introduction to theory of finite differences, and ways that you could manipulate symbols, sort of algebraic ways you could manipulate symbols as although they were numbers. Of course, maybe they don't commute, but it was something that actually I found very beautiful. So I actually learned a lot from that. And then, the actuaries gave me a lot of latitude. The first year, I think, I was told to proofread a text book one of the actuaries was writing on actuarial mathematics, and to work out all of the problems. So I learned a lot from that. And the second year, they had me work on some problems where I had to use a computer. The computer at that time… This was, remember, New York Life Insurance Company, which was the fifth largest life insurance company in the country, and they didn't have any electronic computers. They had some electromechanical computers, which you programed by moving wires around.

They read punched cards and they, you could program up to 150 steps by attaching wires between holes in a board. The connections told the machine what to do at each step, such as reading numbers from some column in a punched card, adding two numbers together and putting the result into a register. and/or punching the numbers held in a register into some other columns in the punched card. I learned that, and it was fun, and they gave me a problem where, in the end, I had to figure out that the way I had to solve it was by turning the cards upside-down and running the cards backwards through the machine and crossing the wires to the appropriate columns on the card. I had to shuttle the deck of cards first forwards and then backwards to run the program. The program was an operation to smooth noisy data. I figured out that you could do it if you turned the cards upside-down and if you put the wires in backwards, it would read the cards properly. You could fool the computer and that was fun. Then, in the third year I was there, New York Life actually got an electronic digital computer. It was, I think, an IBM 705 or 704. I think it used, vacuum tubes. It was huge and it had its own room. Of course, you weren't allowed to enter the room. It was air conditioned and only special people could enter it, but you handed your punched cards through a window and they would put them into the machine. And it had these tape drives that were floor to ceiling tape drives in a vacuum. It was actually a business machine; it wasn't designed for scientific purposes, so floating point was kind of an ad hoc thing there, and I remember it took about 160 milliseconds to multiply two eight-digit floating point numbers together. But still, they could do it. New York Life was just experimenting with it. And they sent me to Fortran school. They had enough faith in me as a student there to send me for three days to Fortran school. That was my introduction to programming. And that was an eye-opener, which helped me later in life. And I wrote a Fortran program to do some data, to do some analysis that they wanted to do. It involved, first of all, to assemble the Fortran program. You wrote it in, you know, Fortran instructions, which were typed on punched cards and fed into the machine.

Zierler:

Bert, I'm not sure if you could hear me, but we cut out.

Halperin:

--I'm back, but it's somehow... Do you hear me?

Zierler:

Yeah, we're back.

Halperin:

Okay, somehow, I don't know what's happening-- Oh, I see what's happened. Okay. Alright, I think we're okay now. Yeah.

Zierler:

So you cut out right when they sent you to the school.

Halperin:

Yeah, so as I was saying, so I wrote a Fortran program-- Hello?

Zierler:

Yep, I'm here.

Halperin:

Are you okay?

Zierler:

Yeah.

Halperin:

It took basically two hours, roughly, for the machine to assemble a simple Fortran program. Of course there were no work stations, so you would write up by hand the Fortran instructions. They would go to some professional typists who would type it onto punched cards and check it. I would bring the cards to the window; they were put in the machine. It would take two hours to assemble a simple Fortran program of maybe, maybe it had 50 lines in it or something like that. And it would come back, and there would be an error of some kind, so you couldn't run it, and you had to patch it by hand. They wouldn't run the assembly all over again, so you patched it in machine code You found the error by getting a memory dump. The whole memory was dumped onto maybe 30 pages of big paper. But anyway, you could see the whole memory of the machine, and you looked for the error and wrote a patch to correct it. The program I wrote had to read a bit of data and calculate some averages and put them into tables. And then, eventually, you had to invert a 30 by 30 matrix. That also took two hours, okay? So that was the way things were in those days. But learning how to use computers and learning what they could do, obviously, was important to me later. And that was my experience at New York Life.

Then the next summer internship I had was in 1961, when, technically, I had graduated from Harvard, because I had come in with sophomore standing. (But I stayed for a fourth year at Harvard, living in the undergraduate dorm. I got permission to do that. So I was technically a graduate student, but I was sort of half an undergraduate and half a graduate. In any case, I was supposed to graduate in 1962, but I graduated in 1961. So, I was class of 1962, but I graduated in '61.

I went to Los Alamos for a summer internship. I applied for a number of places, and I got into Los Alamos. I think I was rejected by several others. And, for a summer job, and there, I think I had wanted to do plasma physics, because that sounded really exciting to me, and I had learned a little bit about it, but very little, at Harvard. But they didn't put me in doing plasma physics. They assigned me to an experimental group that was doing neutron scattering from aluminum, to try to measure the spectra, the phonon spectrum of aluminum. They had a reactor there, down in one of the canyons, which they were largely using to test radiation hardness of materials, but they also used it for scientific purposes, and they had a three-axis spectrometer there. A three-axis neutron spectrometer is a spectrometer for measuring inelastic scattering of neutrons. And they had a group; there were two people, two scientists there, John Yarnell and John Warren, who were working on this project. And I was assigned to them. Of course, I didn't know anything at all about solid state physics. I knew nothing about phonons. So they gave me Brillouin's book to read on phonons and electrons in periodic materials. And I found that very beautiful. That was very influential for me. That got me really interested.

Zierler:

What about that spoke to you?

Halperin:

Well, I never even knew that you… I didn't know anything about Bloch's theorem about quantum states in a periodic potential. So in the phonon example, if you have in a periodic material, you can define a Brillouin zone and you can a wave vector within the Brillouin zone, and [if there is one atom per unit cell] there are three modes at each wave vector, and you have to solve a three by three problem, a matrix problem, to figure them out. But you don't have to mix different wave vectors. You start with a system with an infinite number of degrees of freedom, because it could be an infinite system, but by using this symmetry, you've separated these into a set of smaller problems. That was one thing. And then for electrons, you again, you have electrons moving in an infinite periodic system, and there are an infinite number of them, and they're interacting with each other, in principle, and it seems like a completely hopeless, messy, insoluble problem, but you use Bloch's theorem. If you ignore the interaction between the electrons for the moment, you now find that you have Brillouin zones and you have energy bands, and you have just a discreet problem to solve at each wave vector, and they don't mix. And if you have a metal… I don't think I had understood anything about the difference between metals and insulators…But the fact is that if you have a metal, you have a Fermi surface, and you can actually map that Fermi surface. You could look for effects of the Fermi surface in phonon spectrum. (That wasn't in Brillouin's book, but it was something that came out later). But I learned these ideas at that time, and they were surprising to me. That a complicated system like a crystal with lots of electrons could actually be simplified to the extent that you could talk about mathematical problems to solve, to really help you understand what was going on in them…

Zierler:

What was the quality of the instrumentation at Los Alamos? Were you exposed to stuff that was not available at Harvard?

Halperin:

It was certainly not available at Harvard. Los Alamos was not the best in the world in the field, but inelastic neutron scattering was something that was new then. I think Bert Brockhouse in Canada was the leader of the field, and they had a much more powerful reactor than Los Alamos had. So Los Alamos was this sort of second cousin, but they were working, and they found some interesting things to do. They could compete because only a few places in the world were able to do it. MIT had a reactor. I don't know if it was in operation at the time, and I don’t know if they had a three-axis spectrometer. Cliff Shull was at MIT and did much of his work there. I think some of it was going on about the same time, but I wasn't particularly aware of it, certainly. I didn't know anything about it.

Zierler:

And did you feel at Los Alamos like, was the Cold War palpable? Did you feel the sense that there was a national security component to Los Alamos, or was that really not something that you felt?

Halperin:

Oh yeah, we felt it. It didn't influence my work, but I certainly was aware of it. And there was a culture of awareness. During at the time I was there, there was a moratorium on nuclear tests. I think it was originally unilateral, but they had ceased testing. Both the US and the Russians had ceased atomic tests. There was not a treaty, but they had both done it sort of unilaterally. And some people at Los Alamos were certainly unhappy about it.

Zierler:

Right.

Halperin:

About that.

Zierler:

Right.

Halperin:

And then, I think, during the summer I was there, the Russians broke the test agreement, they tested something, and the US, of course, started up again, and not everyone at Los Alamos, but there were a fair number of people at Los Alamos who were overjoyed at that. We were certainly aware of that. I'm not sure about what the feelings of John Yarnell and John Warren were, I have no memory of that. But there were people who were happy. There were two reactor operators who ran the reactor, women who lived at Los Alamos, who had been drivers. They had been there during the war as drivers. They drove jeeps and cars, drove generals around, and stuff like that. They were very patriotic and they were very happy that this testing ban was over, that we now saw that this was an impossible thing. So we were certainly aware of that. I remember one other thing, then. Someone posted on a bulletin board, there, an article from some newspaper or other saying that the Russians were working on a neutrino bomb. They were working on this, and neutrinos were so powerful that they could penetrate the earth, and they could direct the neutrinos at us from Moscow and run them right through the earth and hit us in the US. (laughs) I didn’t know if that was put up in jest, or whether someone took it seriously, but I remember that vividly.

Zierler:

So it sounds like Los Alamos was very formative for you in terms of what kind of physics you wanted to pursue?

Halperin:

Yes. Yep.

Zierler:

Did that influence the kinds of courses that you... Well, wait a minute. You didn't, you were... Did you go back to Harvard and continue taking courses?

Halperin:

Yes.

Zierler:

Oh you did.

Halperin:

Right.

Zierler:

But as a graduate-- Or as a semi-graduate student?

Halperin:

Yes, I was a first-year graduate student at Harvard technically. Although I had intended all along to probably transfer out, I stayed there for a year because I wanted to get my fourth year as an undergraduate, sort of. And I also took a German course. I didn't want to just do physics, so I took a German course. But I was taking basic first year graduate courses, and I did not take a solid-state physics course at Harvard. I think it was offered, but I was still taking prerequisites at some level. I could have taken an undergraduate course., but anyway, I didn't study solid state physics formally until I went to Berkeley.

Zierler:

Right, right.

Halperin:

But I already was interested in it when I applied to Berkeley for transfer. I applied there partly because I knew the work they did, they were doing solid state physics there, and I had already decided that that's probably what I wanted to do when I applied.

Zierler:

Did you only apply to Berkeley?

Halperin:

Yes.

Zierler:

And as you were saying, it's because you knew of their reputation in solid state physics?

Halperin:

Well, to be perfectly honest, I applied to Berkeley, or I decided I was going to apply to Berkeley because I was tired of the Massachusetts weather, and I heard great stories about the weather in California, and I thought that that should be an important important factor. Now, I knew that Berkeley had a great reputation. The reputation may have been based on developments that were partly out of date, but I didn't know that.

Zierler:

Yeah.

Halperin:

And it had a great reputation, it had great people. I didn't know about solid state physics when I thought about it originally. Berkeley didn't have a great reputation in solid state physics, no place really did. But it did have good people in solid state physics. And it--

Zierler:

Now, geographically, why not CalTech or Stanford?

Halperin:

Yeah, I also thought about CalTech and Stanford, but I think Berkeley actually had a kind of better reputation at the time. I don't remember exactly... I might have applied to some of these other places, but I don't think so. I think I only applied to Berkeley, and maybe by the time, yeah, by the time I actually filed my applications, I think I did know. But I knew because I asked around, you know, "are there any good solid-state physics people there?" So it may well be, I think it probably is true, that I had a sense that Berkeley was better than CalTech or Stanford for solid state physics at the time. And for solid state theory, at the time. And that's probably why I decided to apply there.

Zierler:

But you said, Bert, you said previously that no one really had a reputation? You said previously no one really had a reputation in solid state physics.

Halperin:

Yeah, Bell Labs was the place. I mean, solid state physics wasn't that popular really in universities at the time.

Zierler:

And does that mean that it was, when you say "not popular," is that because it was not particularly developed as a field?

Halperin:

Yeah. Well, yeah. There weren't that many people doing it.

Zierler:

Why do you think that is? What accounted for that?

Halperin:

Well, okay, so people were, you know, you date back ten years, people were tremendously excited about nuclei and nuclear physics, and then it became high energy physics, and that's where all the romance was. And solid-state physics was considered dirty. Several people called it "dirt physics"-- I mean Pauli called it "schmutz physics." You know, it had not much reputation in universities. The people who were doing the most exciting work were people at Bell Laboratories, for example. Bell Labs and IBM were doing good work. They had more going on there than all the universities in the US. And at universities, a lot of it was put into applied physics. There was an applied physics department at Harvard for example. [Actually, a subject area within a Division of Engineering and Applied Physics.] I went back to Harvard later; Henry Ehrenreich was in the applied physics department. And Paul Martin was in the Physics department, He was there when I was in undergraduate, and he started doing condensed matter physics at the time, but he had started out in particle physics. And Vleck, of course, was there. And he later became head of the department of applied physics, but he was also in the physics department. There certainly was solid state physics going on, but it was a small part of the overall effort. The focus was much more on nuclear and particle physics, and that's where the theoretical challenges were supposed to be. These were the fundamental things, they thought. And solid-state physics wasn't thought of as being so fundamental. That was the attitude. But, and I think that was true in many physics departments. CalTech, I don't think, was that interested in condensed matter at the time, though certainly Feynman was interested in liquid helium and polarons. So he was interested in it, but in any case, as I say, I decided to go to Berkeley, there were other great places. You know, I could've looked at Chicago. There were places I could have looked at, especially before I decided that it was solid state physics that I wanted to do. But I did say, "Well, what the heck, let's go to a place where the weather is good." The irony is, of course, that after I was at Berkeley for two years, my advisor left and went to Princeton. And I went with him.

Zierler:

Right back to the East coast.

Halperin:

And the weather at Princeton was not very much better than it was at Harvard.

Zierler:

Now, you're talking about, you're talking about John Hopfield?

Halperin:

Yes I am, yeah.

Zierler:

Now, did you connect with John before you got to Berkeley, or you only developed that relationship once you arrived in Berkeley?

Halperin:

Okay, so I don't... After I had applied to Berkeley, and maybe I was already admitted, I'm not quite sure, I spoke with Ray Orbach, who was at that time, he may have been assistant professor, maybe a post doc. I think he was an assistant in applied physics at Harvard. He may have been a post doc. He had been at Berkeley. (He later, of course, became well-known, and was chancellor at UCLA and so forth. And high up in the energy department. But he was a young guy, and I asked him, and I knew he had been at Berkeley, so I asked him, you know, who's good there? And he told me, of course, Kittel was very well known. He told me about Kittel and said he was very good, and he said there was a new guy there who had just come, who was a real, you know, upcoming guy, named John Hopfield. I, of course, never heard of him. And Orbach said… of course, he was a very politically astute guy.. he said, "Why don't you write to Hopfield and tell him you're interested in his work?" And I don't remember whether I actually did or not. To me, that seemed like that's not something that one should really do. That seemed pretty forward. But I think I might have done it. So I might have established that connection. But when I got there, I, you know, I was taking courses for the first year.

Zierler:

And where was he coming from? Was this his first job out of being a post doc?

Halperin:

He was at Bell Lab. He was a member of the technical staff at Bell Labs.

Zierler:

Okay, okay.

Halperin:

And then he went there. And he was, I think, in his second year there. And I was like his third student or something like that kind of thing.

Zierler:

And what kind of work was he doing at the time?

Halperin:

So, he was interested in semiconductors, and the problem he eventually gave me was to try to understand what was known as Urbach’s rule. It had to do with optical absorption, not so much in semiconductors as in insulators like alkali halides. And so he was certainly interested in optical properties, optical absorption of insulators and semiconductors, and Kittel was interested in magnetism, so there was sort of a choice. When I got there the first year I was just mostly taking courses, but then I had to take an exam to get into the solid state theory group. It was a joint eight-hour exam that the two of them gave to weed out students, and if you passed the exam, you could be a candidate and could work with one or the other of them. I passed it, so I could then choose between the two of them, and I interviewed both of them. And I was, you know: Did I want to work on magnetism? Did I want to work on insulators? I eventually chose Hopfield. So the beginning of second year at Berkeley, which I guess was my third year of graduate school, I started doing research and it was on this problem that he gave me.

I should say, about that exam: I still remember it was an eight-hour exam, and it was written. It had four problems, and they graded it. it was 65 points to pass, and I thought I had aced it. But no, they took off ten points because I didn't know the value of h-bar, ten points for this, ten-- So I wound up with a 70, and I remember Kittel telling me, "Well, alright, you passed. So you can join our group." But I was kind of annoyed that they had taken off so many points for minor things. Kittel said, "Well, you should know these things by heart, because you may be traveling on an airplane and you want to work. You have to know them." I had never thought that I would frequently travel on an airplane. I had almost never been on an airplane, I never was on an airplane until I was 19, and I'd been in an airplane maybe three times at this point in my life, and the thought that I would be traveling often on airplanes seemed preposterous to me anyway. But yes, I remember that.

Zierler:

What was Hopfield's style as a mentor? Was he hands on, hands off?

Halperin:

He was pretty hands off. It was quite interesting, and I think about that. I didn't see him very often. He gave me this problem; the problem was to find, to understand, Urbach's rule, which was the low-energy tail of absorption below the absorption edge of an alkali halide, say potassium chloride or potassium bromide or something. It has a principal absorption edge, optical absorption edge, where you can absorb a photon and produce an exciton, which is a bound state of an electron in a hole. And that exciton is bound by about half a volt, so it's well below the electron-hole continuum. And in principle, you have to conserve momentum, so you, it should give you a sharp absorption line. It's more complicated because you really have to solve the combined problem of photons and excitons, and you get polaritons and stuff, but there's a threshold. And there should be no absorption below that threshold. But in fact, that's not the case. There is some absorption. The absorption coefficient falls off exponentially with photon energy, as you go below the threshold. And it gets very small rapidly, but it extends maybe for another half a volt below the threshold and it falls off by eight orders of magnitude or ten orders of magnitude. And if you plot it, it falls on an exponential curve with amazing accuracy. So in ten decades, it seems to fall in a straight line on a logarithmic graph, and the slope has a temperature dependence. Hopfield had some ideas of how it might come about, which I think were wrong in effect in the end, but he gave me that problem, which was not an easy problem. He didn't give me a simple warmup problem. He gave me this problem and he gave me some references and said, "Go work on it." And I went and worked on it. And I came back, I was stuck, and he gave me some more hints. But I saw him rarely. I certainly didn't meet with him every week. Whenever I wanted to meet with him, he was free, but he never sought me out. He never asked, I don't remember him ever asking, how I was doing. And at some points, I got stuck and I went to him.

I should have said it earlier, but Hopfield suggested at the beginning that the basic idea was that the exciton interacts with phonons, and you have fluctuations. For example, there are thermal fluctuations of the phonons, because you have finite temperature, and with thermal fluctuations, the exciton sees something like a random potential. So you have regions where the energy is lower and higher, and that can give you your tail. I don't know exactly how, to what extent I realized that by myself. I'm sure Hopfield realized it. He gave me some papers to read which kind of hinted at it, that if you treated it in the right way, you know, if you thought about it the right way, you could neglect the energy of the phonons and think about it as, because they're relatively slow, as static defamations, and you're trying to solve a problem which is a particle in a random potential. And that was, in some sense, what I focused on. I'm not quite sure to what extent I realized that all by myself, and it wasn't necessarily the way he wanted to look at it. I think he maybe wanted to think the phonon energies were important, but that's what I wound up thinking about, and I was trying to solve that problem, when I got stuck. And so at some point I got discouraged. I said, "What if I can't solve the problem?" And he said, "Well, don't worry, there are plenty of other related problems. If you can't solve the problem, there are a lot of other problems in optical absorption, and this would be a good training for you."

So that was one point I took from him. And then at some point, he said, "Okay, if you can't solve the problem in three dimensions, maybe you can solve it in one dimension. Problems in one dimension you can always solve. They're easy." Well, so I said, "Okay, let me try to do that." But it turned out to be much harder, I think, than he thought. But I did manage to solve the problem, and I was very proud of it. It wound up being my first published paper, and it involved some neat mathematical tricks and things. It was not by any means a straightforward extension of stuff that had been done before. And it involved some tricks and ideas that I think were new. And also, I was able to use some slightly obscure math that I had learned in an applied math course in Berkeley, and I was very proud of it. So I wrote the paper and it is still a paper I'm proud of, although it wasn't terribly important, really, in retrospect, but it was very satisfying. I set out to solve a well-defined mathematical model, and after much work, I was able to find an exact solution for the Greens function in this problem. That’s something that was actually rediscovered independently by some Russians 15 years later, which maybe shows how little-known the paper was.

Anyway, it was quite interesting, and I was able to learn from it what was going on in the low-energy tail, and that gave me some ideas, so I was able to then go back and start thinking about the three-dimensional problem. And I started, I went back... I basically did this work while I was still at Berkeley, within the one year, 1963 to 4 when I was at Berkeley, before Hopfield left. So I went back to the three-dimensional problem, and I was getting some results that weren't right. There, he did help me by pointing out some mistakes I was making. And some of the things I was ignoring. That was helpful. And I had some ideas that were sort of beginning to give me something that looked a little bit more like the right answer, and began to give me some idea to how to proceed. Using these things, I was beginning to see how I might understand the tail of the one-dimensional problem, that was the point, so I could also think about the three-dimensional problem.

And then, Hopfield got this offer from Princeton, and he left Berkeley in June of 1964. He got me a summer job at Bell Laboratories, and I decided I would follow him afterwards to Princeton, where I moved in September. So over the summer, through Hopfield's good influence, I managed to get a summer internship at Bell. And at that time, again, Bell mostly didn't take students, but he wrote a strong letter, sent it to Mel Lax. Apparently, Mel Lax lost the letter. But he called Mel Lax and convinced Mel to take me on. And so I was taken on, and that was very important, because Mel Lax actually had been working on a mathematically similar problem. He wasn't interested in optical absorption by excitons; he was interested in the low-energy tail of electron states in a semiconductor with disorder due to impurities. But again, it was electrons in a disordered potential, and he had some ideas which were complementary to mine. And we teamed up, and we eventually wrote this paper together, actually a couple of papers, but our first paper on the low-energy tail of an electron in a gaussian disordered potential was the thing that was probably the most help to get me job offers, and it was what made the difference. That was a good start to me career. It turned out that some of the work, our ideas, were anticipated by Ilya Lifshitz in Russia, but at least I didn't know about it. I don't think Mel knew about it in the beginning. Eventually, we learned about it. Lifshitz had done, of course, very beautiful work, and he's very well-known for that, for what he did on low energy tails. And we had sort of independently, at least, discovered some of it. Not all of what he had done. But we also went beyond what he had done in several respects.

Zierler:

Was it an easy decision to follow John to Princeton?

Halperin:

Hmm?

Zierler:

Was it an easy decision to follow John to Princeton?

Halperin:

No, I was worried about the weather and stuff. No, seriously, it was not an easy decision. I don't remember it being easy. No decisions were ever easy for me, so I can't believe that it was easy, but I think that it was an easier decision than many that I have had to make. I thought I should not try to switch thesis advisors or topics This was of course before, I had to make that decision before, I had done the largest part of my thesis work. I may have done the one-dimensional stuff, but I certainly hadn't solved the three-dimensional problem.

We never did completely explain Urbach's rule, by the way. I can’t say we solved that, but we found that, yes, we could explain why things were kind of exponential. But why they should be linear and not go as exponential of, let's say, the energy to the three-halves power or the one-half power or something in between, we couldn't explain. In one dimension, I got something like exponential of minus the energy to the three-halves power divided by the temperature, and in three-dimensions, for the simple model we considered, you got exponential of minus the energy to the one-half power, divided by the temperature. So it was exponential but not linear.

Zierler:

Now, did you attempt to integrate yourself within the physics community at Princeton, or it was really more about just finishing your work and defending at Berkeley?

Halperin:

Well, of course, I wasn't taking courses. I was a visiting graduate student. I had an office, I had a desk up with the other graduate students, and I certainly had friends with the other graduate students. There was one other graduate student doing condensed matter theory, and there was an assistant professor, actually, doing condensed matter theory, but there was not much condensed matter theory at Princeton. Hopfield was brought in to do that. There wasn't much. There were some experiments, but not much. You know, I went to talks and colloquia, and I had graduate student friends, but I was married, we had a kid. So, I was somewhat isolated in that sense. We weren't allowed to live in married student housing. I was allowed to pay tuition to Princeton, but not to live in married student housing. So we lived off-campus, and because of that, my integration with the social life was somewhat limited. And I wasn't taking courses. I don't think I even audited classes. I was working on my thesis. I had communication with Mel Lax. We were doing follow-ups on our summer’s work.

Zierler:

And what was the date of your dissertation defense?

Halperin:

So okay, my thesis would have been finished around May 1965. The defense was entirely by mail. There was no actual defense. I had to submit it to the committee. The committee read it and approved it. There was no--

Zierler:

No oral?

Halperin:

No oral. No oral.

Zierler:

Did you have to go back to Berkeley for this, or you did it all from Princeton?

Halperin:

All from Princeton, yeah.

Zierler:

Uh-huh. And who was on the committee besides John?

Halperin:

Well, I'm sure that Kittel was on it, but I don't remember who else.

Zierler:

Would it have been another Berkeley professor or possibly someone at Princeton?

Halperin:

No, it would have been someone at Berkeley, I think.

Zierler:

Uh-huh. Okay, so at this point, you defend, and then what are your options? What's your plan at this point? What do you want to do next?

Halperin:

Yeah, so. I wasn't quite sure what to do. When I had been at Berkeley, and I was trying to decide between Hopfield and Kittel. Kittel told me, "Well, if you come and work with me, and if you're successful in research, (and just because you've been doing well in courses doesn't mean you'll be successful in research; there's about a maybe 50/50 chance that you'll do well) but if you do well, then you have two choices. You can get an assistant professorship at a good university, or you could work at one of the top industrial laboratories." Which, in order, he listed as Bell Labs number one, I believe GE was two, and IBM was three, or maybe it was the other way around. Those were my choices that he offered me. And that stuck in my mind a little bit. Then when I got, when I finished my... So those were sort of the longer-term plans, but as I was finishing my PhD, at Princeton, I applied for an NSF, a one-year postdoctoral fellowship, which was then available. I don't think that's available so easily now. There are of course graduate fellowships, I had an NSF graduate fellowship, but postdoctoral fellowships are not available-- I don't think they have them in condensed matter anymore. They may have them in some fields. And that would have enabled me to go wherever I wanted to. Hopfield had spent a year in Paris and he thought that was a great experience, so Hopfield suggested that I apply to the École Normale Supérieure in Paris. I got the NSF, and I was accepted in Paris, and I spent a year in Philippe Nozières’s group at the École Normale. I decided, well, that'd be a fun thing to do. And I had never been even out of the country before, and--

Zierler:

How was your French?

Halperin:

Well, of course, I'd studied it in elementary school, in junior high school, and in high school. So I was probably at the level of somebody who had... I could have certainly gotten into a second-year undergraduate course or something like that. And I guess, as I said, I was reasonably talented for it when I was in junior high school. By the time I was in high school, I think I was less serious about it, but I got an A in it, so I knew some French. My wife had also studied French in high school and had taken at least one course in French in college. And then, when we decided we were going to go to France, we hired a tutor for maybe a few months. We had, you know, lessons a few hours a week to bring us up to speed.

Zierler:

So besides the cultural, you know, attraction of it, what scientifically was interesting about what was going on in France at the time for you?

Halperin:

So, as it turned out, I worked very little with Nozières; he was very busy. There were a lot of undergraduates around. And graduates, there were post docs and graduate students, rather, who were doing interesting stuff. I remember them most. There were lectures, I remember Cyrano De Dominicis gave a set of lectures on many-body theory and Feynman diagram-type techniques, and so forth. I learned a lot from that. Also at that time, de Gennes was doing beautiful work on superconductivity. He was not at the École Normale, he was at Orsay, but we went back and forth somewhat. And there was a post doc, a woman in Nozières’s group [Odile Betbeder] who had worked with de Gennes. had done superconductivity work and maybe was continuing to work on it with de Gennes and I learned a lot from her.

And Paul Martin spent the spring, a semester, there, and I worked with him quite a bit. He was from Harvard, of course, and I had known him from Harvard because I had taken a course from him at Harvard, and he was my nominal advisor in my final year at Harvard. He signed my study card as a graduate student at Harvard. And I had spoken with him and I had learned from him. He taught a course in electrodynamics, which I had taken from him, and I learned a lot from that. And he knew about me, I think, from people at Bell Labs. And we did a lot of work, we worked on problems related to fluctuations in two-dimensional superconductors. And we did some pretty nice work, but as it turned out, we discovered that it'd all been done before. We, sort of, had gotten to the point where we were about to write things up, and then Paul said, oh, it turns out that Kadanoff and Kane had done essentially similar work, and there wasn't enough new to really pursue it. But I learned a lot about two-dimensional systems and fluctuations and vortices and stuff from it. So it turned out to be useful. I learned things from that. I continued to work on disordered system problems with Lax, long-distance, from there. And I wrote a review article on one-dimensional problems, which took a fair amount of my time, when I was there.

Were these the reasons I went there? No. I went there because I knew that there were good people there. Hopfield told me it was good, that there would be good people there, and I figured I'd learn something new. I wasn't planning to particularly follow up on anything specific. I guess maybe I did think that I'd learn something about superconductivity there, and many-body theory. So I probably had some general ideas, but mainly I just said, "Well, you know, this place has a good reputation." Nozières’s was a very good person. It just turned out that he was so busy that I really didn't have much time with him. And he had six other people working with him, so in the end, I didn't interact with him that much, but he was certainly a reason for applying there, and a reason, certainly, that Hopfield recommended it. It wasn't just the cultural thing. But also, it was an entree into Europe more generally, not just France. Not just École Normale, but France, Orsay was certainly a very major player in both experiment and theory at that time. And maybe, yeah, Germany was beginning to be, and so forth. And, also, I went to England from there.

Zierler:

And when did Bell Laboratories come together for you? Did you put this together from France, or you came back to the States first?

Halperin:

Well, Mel Lax wanted me back. He was the head of the theory department at that point. So Mel Lax certainly tried to interest me in coming back to Bell Labs from the very beginning. And I also, I'm trying to remember how it worked. I certainly went for some interviews at other places before I went to Paris, I did look around for jobs for afterwards. I know I went for an interview at GE, I remember that interview. And I think I went to IBM as well. But Bell Labs at the time was the one of the three places that seemed the most interesting, and it seemed like it made more sense to do that than to go to a university and have to worry about tenure and, you know, and teaching and so forth. And from the point of view of doing scientific research, Bell Labs was at least as good as any university-- arguably much better. And Mel Lax certainly put a good face on it for me. But I did also think it worthwhile to interview other places. And I think I had offers from all three places. At Bell Labs, it would've been basically another, a second post doc effectively, for the first year, but Lax assured me that it would almost certainly lead to a permanent position.

That seemed to make sense, and I sort of assumed I would do that. But after I was at Paris and worked with Paul Martin for a couple of months, I got an offer of an assistant professorship at Harvard, and that was tempting because, you know, of all the places-- By this point, having been an undergraduate at Harvard, and Harvard did seem to be number one in my mind. And going back to Harvard as a professor really did seem a dream possibility. Can't do better than that. I had, I'm sure, an overblown view of Harvard, but in any case, you always have a kind of affection for your undergraduate place. So that was kind of tempting, but you know, I knew that there was no guarantee of getting tenure there, and it was a little hard for me to see that I would. And Mel Lax got me an offer at Bell; actually he got me an offer as an associate member of the technical staff. So I would be technically an employee, and would have employee benefits, but I wouldn’t have permanence. Well, there's no such thing as tenure at Bell, but there was a notion of permanence. And he said there was a very good chance I'd get it. And that there were a lot of advantages. I could always go to a university after that. So I decided that it was better to go back to Bell. That was not such an easy decision.

Zierler:

So you went in thinking that you could always go back to a university if you wanted? You didn't feel like, by going to Bell Labs, you were turning your back on academia?

Halperin:

Oh absolutely not, no. That was standard, people were flowing through it all the time, and Mel certainly made the point that this would be a great place to get an academic job from, and typically you would get an offer of a tenure appointment.

Zierler:

Right.

Halperin:

So you didn't have to go through the tenure process. And you could stay, you know, you had no deadlines. And that's, you know, what happened. I mean, actually, it was not an easy decision, as I say, decisions didn't come easily to me, but that's what I decided.

After I was at Bell Labs for three years, Harvard got me to go there for a year. I went, I spent '69 to '70 as a visiting instructor at Harvard. I got a leave from Bell Laboratories for a year, and I taught there. I taught a course, and had a student and so forth. So I had an introduction to academic life, and they actually were prepared to make me a tenured offer, to bring me there. It hadn't gone all the way through, but it got approved by the department, and gotten fairly high approvals, as I understand it. But in the end, before I got a formal offer, I said, no. I decided I wasn’t ready to leave Bell for a university. This was 1970. There were, you know, there were a lot of reasons why universities were not so attractive at the time. It was not quite as bad as '68, but there were sit-ins. They actually closed the university down in spring 1970. They told all the students that they didn't have to take final exams, but they could take their makeup finals in the fall. They could, or, they could skip the exam and get a grade based on what they had already done in the course. Yeah, the idea was, well, that students should be free to go to Washington and protest the war in Vietnam. I don't know. It wasn't the greatest of atmospheres, and that was certainly a factor. It was also looking a little harder to get money for grants and so forth. And I found that teaching took a lot of time, and I wasn't really sure that I had enough ideas at the time that I wanted to have a flock of graduate students. So, again, it was a hard decision for me to give up, in a sense, what had been a dream of a tenure appointment at Harvard, to go back to Bell Laboratories, where I was not worried about having a job, but Ii still was giving up something that had a lot of permanency for something that was a little bit more uncertain. But in the end, I decided that I wasn't really ready to do it.

It was only five years later that I was again given an offer from Harvard, and I said, by this time, I felt more capable of having students and benefitting from students and teaching at the same time. And, also, I had more doubts about whether the ivory tower at Bell Labs could really last. And you know, there had been economic hardships there when the period of huge inflation... I remember having actually a luncheon with the president of Bell Labs at the time, who was Bill Baker at the time. He said, "Well, you know, we have to pay 14% interest now, and AT&T has to buy a lot of copper to make wires and they're borrowing money and paying 14.5% interest. Can I show them that investments in research can pay off at the rate of 14.5%. That's pretty hard." And, you know, it was. They were still supporting research, maybe slightly less. They were putting a lot of pressure on people to work on silicon. The future wasn't so clear. I don't think I understood how bad it was eventually going to be, but it certainly was clear that Bell Labs, you know, that it was not certain that it was going to continue forever. There was also the issue of growing old at Bell Labs. People had said, you know, that a lot of people at Bell Labs went up in management. There were great opportunities to go up in management. A lot of the management at Bell Labs had come from research. But I wasn't really interested in that. And then, what happens if you lose some of your interest in research, or you are not as good at it as you get older? What do you do? If you're at a university, you can still teach. You know, there's a lot more flexibility there. And that held some weight with me. The idea of living in the Boston area rather than Summit, New Jersey also had some influence. I thought that Summit was a little bit isolated in a way, and so that had some influence. My wife saw better opportunities in the Boston area, in some ways. Those also had some influence. But it was, again, that was a very difficult decision to finally leave the ivory tower for the real world, as it were.

Zierler:

And when you got there, did you pick up with Mel Lax on the research that you had done previously, or were you working on new projects?

Halperin:

No. I'm trying to remember, [When I went to Bell labs in 1966] I think we did complete some work there, but I don’t definitely remember writing a paper with Mell, with him, when I was there, but no, he was not that much of a factor. I worked mostly with other people.

Zierler:

And what was the culture of collaboration like at Bell Labs? Could you get yourself involved in any number of scientific projects, or did you really have to stay in your own lane?

Halperin:

Oh no, I don't know what staying in my own lane would have been. No, not at all. It was very interactive. You went to seminars with people, you had lunch with them, you saw them in the halls. I certainly got interested in what they were doing. People came to me a lot. i guess I got a reputation of being someone who could solve problems. I know that Pierre Hohenberg, whom I worked with a lot, said that he sought me out partly because he heard of that, and I think some of the other people may have sought me out. They had ideas and problems that interested them because of experiments or something else, and they said, "Well, maybe Bert Halperin would have some ideas on how to solve those problems." And so, yes, I was sort of a problem solver, and so a lot of people came to me. I had no shortage of problems. Which in a way was, you know, at the very beginning when I wasn't so sure if I could think of my own problems, because a lot of them had come to me from other people. And it was certainly, I don't know, I don't think I wrote any papers by myself when I was there. Maybe I did, perhaps some review paper or something like that, I probably did write a few papers by myself. But research was almost all done in collaboration, sometimes with experimentalists as well as theorists.

Zierler:

And who were some of the major scientists who were at Bell Labs at the time?

Halperin:

Okay, so, again, theorists: I guess the two really outstanding theorists there were Phil Anderson and Conyers Herring. Conyers Herring was older and had sort of an encyclopedic knowledge and great insights. He had done wonderful things in magnetism before the war, even. And after the war. And he was very knowledgeable and he read, it was incredible, he read everything. He read Russian. He knew what was going on. He had this briefcase full of index cards, where basically everything of interest in condensed matter physics, he had a card about, and he could get you references. He was fantastic. And Phil Anderson was younger, of course, but still significantly older than me, and he had already done this beautiful work on solving localization. But had ideas about everything. He clearly was one of the, I mean, in my view, was the outstanding, most original, brilliant theorist in condensed matter over a period of decades, starting from, say, '58. Basically, in the second half of the 20th century. Certainly, from his work in 1958 on through the late 80s, he was the person who had the greatest ideas: you know, the Anderson model for this, the Anderson model for that, You could think of almost every major problem, the localization problem, and Kondo problem, he had an Anderson model. Spin glasses, there was the Anderson model, Edwards-Anderson model in that case. Localized moments, the Anderson model. So he was--

Zierler:

And was this because he was such a deep thinker? What was his secret, as you understood it?

Halperin:

Well, he was brilliant. (laughs) He just died, but yes, he was brilliant, he had very...why, he could read a lot, he could digest experiments very quickly. He had fantastic taste. I don't think he was a brilliant mathematician, exactly. I don't think he ever... I mean, he certainly understood math, understood gauge theories and stuff, but math wasn't his strongest point. He wasn't solving very hard mathematics problems. He could ask himself what was important, what was really going on, what were the things we really need to understand, what's the simplest model that I can write down that embodies the physics that helps me understand what's going on? And then solving these simple models, which he could usually solve using relatively simple ideas. Sometimes they came out very obscurely, in the way he wrote things up. They were not always easy to understand, but he sort of understood them and didn't feel tremendous obligation to explain them in a clear way, so he could go on and work on another problem. So sometimes he made mistakes, sometimes he was disparaging of other people's contributions, but in terms of sheer insight and brilliance, I never met anyone who could compare with him. You know, maybe Bardeen in his time. I assume Landau in his time could have. De Gennes was, of course, extremely original in his own way. But I think Anderson had the most insight. I think I wrote only one paper with Anderson. I didn't interact with him that closely, but he certainly set a standard and I certainly spoke with him about things and learned from him. And I never wrote a paper with Herring, either, but they set the atmosphere. Mel Lax was another outstanding physicist, not probably at quite the same level as these other two, but someone who was maybe under-appreciated in a sense. He had great insights into disordered systems, into lasers. He did a lot of very interesting things. But as I said, Lax sort of went in a slightly different direction than I did, but he was a leading influence there. And he had a very good taste for people. Well, I should say that, he hired me, but I think he helped bring in a lot of good people at the time.

And there were a lot of very good young people who have gone on to do great things there, that I interacted with. So I did write papers with Maurice Rice, and of course, Pierre Hohenberg was very important to me. Patrick Lee came a bit later, and he was doing great, was very brilliant. There was Bill McMillan, who was very brilliant, and I didn't really get to work closely with him, but he set a standard. Jim Phillips was there, who certainly was brilliant but I never worked with him, and he wasn't easy to work with, exactly. And we had different interests, anyway. Bill Brinkman was there doing beautiful work. There were other good people-- Evan Kane had done very nice things. And so on. I worked with Dean McCumber, who did some nice things, but sort of rapidly went up in management and didn't do too much research.

Zierler:

So in looking back in your tenure at Bell, what do you see as your most important contributions and work while you were there?

Halperin:

Well, there's no question that the most important work I did there was the work I did with Pierre Hohenberg. Critical phenomena, particularly dynamic critical phenomena, although some of it also involved static critical phenomena. That was an occupation that in the end continued after I left Bell, but together we wrote, I think, like 16 papers together. It's certainly what established my reputation, without question. Although I'd gotten some attention from the low-energy tail stuff. But the thing that in the end cemented my reputation, I think, was this work. It wasn't the only thing I did at Bell, but it was this central theme of what I did. Other things were really quite unrelated to it.

Zierler:

Yeah. And what were some of the major research questions that you were working towards?

Halperin:

You mean in addition to what was-- Should I explain what the problem, what we were trying to understand was with Hohenberg?

Zierler:

Exactly.

Halperin:

Okay, so this was in the late 60s, we got started on it. And so there was a lot of effort to understand critical phenomena. “Critical phenomena” tells you what happens near a critical point, such as, the simplest to understand, the magnetic critical point. You have a ferromagnet where the spins are aligned on average in a certain direction, at low temperatures, and you can realign them by applying a magnetic field, but even if there's no magnetic field, a large fraction of the spins in a domain, they're all pointing in the same direction. Something makes them want line up. There's forces that make them want to line up, and even though you have finite temperature and there are fluctuations, the fluctuations cause some of the spins to flip, but there's still on average a magnetization. And if you heat it up enough, you hit what's called the Curie point, which in iron is, I don’t know, 1400 degrees Centigrade or something, where the magnetization vanishes. And at this point, entropy is much more important than energy, and at high temperatures, the spins are essentially random. Half of them are up, half of them are down, or they're pointing in every which direction. There are correlations at short distances, the two nearest neighbor spins are likely to be pointing in the same direction, but the correlations between two spins fall off exponentially with distance. So they could be completely negligible once you get more than a few nearest neighbors away.

And there's a transition between the states, which is called the critical point, at which the magnetization goes to zero at some power law of the temperature. There's a simple mean field theory, the Curie-Weiss theory, that said that the magnetization should go away as the square-root of the temperature difference TC minus T, where TC is the transition temperature, and then above that, there's no magnetization. Above that, there's a correlation length and a magnetic susceptibility which increase as one approaches TC. And the simple mean field theory, or Landau theory, said that the susceptibility, let's say, would diverge as 1/ (T-TC.) The correlation length would diverge as 1/square-root of (T minus TC). So there were power laws that were predicted, and experiments had shown that they weren't right in three dimensions, and the exact solution of the two-dimensional Ising model, which came from work in the 1940s, showed that this mean field theory wasn't right. So something else was going on, and it was a great puzzle to understand what really would happen in three dimensions. Why did mean field theory not work? And there were scaling ideas, there were various ideas that sort of suggested that what happens as you get close to the transition temperature is that it's very easy to get long wavelength fluctuations. You get these long-wavelength fluctuations that mean that things don't fall off as the way you'd think they do.

The long-wavelength functions are important enough that they cause breakdown of this mean field theory. And what happens instead wasn't quite understood. But it seemed that you could at least relate various quantities to each other with these scaling ideas, which Kadanoff and Fisher and others had contributed to, and they explained why the susceptibility… -- they didn't explain, but they at least correlated ideas as to why the susceptibility diverged the way it did, and the way the correlation length diverged in the way it did, and the way various other correlation functions fell off. And these were called scaling ideas, and they were obtained by sort of saying you could start with a, say, an Ising model of magnetism, which had spins on every lattice site, and you could integrate out many of the lattice sites and just look at the long wavelengths, get rid of the short wavelength fluctuations, reduce the number of degrees of freedom, and wind up with some kind of effective Hamiltonian for the long-range degrees of freedom that would be different from the original Hamiltonian, but there'd be some rules for constructing the new one from the old one, and these would lead to some kind of scaling ideas. And somehow that would hang together and explain things.

And all of these properties that people were looking at were static properties, they would be properties like the correlation function between two spins at the same instant of time, or properties like the magnetic susceptibility, which is related to the change in the free energy when you apply a static magnetic field. So these were all things that you could calculate if you could solve for the thermodynamic density matrix, the thermodynamic ground state in a magnetic field, let's say, at a finite temperature. You could compute the magnetization and how it depended on temperature in magnetic field, or you could compute the pair correlation function and these properties. The Ising model has no quantum mechanics in it at all, but if you went to a model that had quantum mechanics, the quantum mechanics was not important, because the important fluctuations would happen at long wavelengths and low energies, where, basically, the timescale would be slow, so the frequencies would be small: h-bar times the frequency small compared to the temperature. So basically, the feeling was, certainly for the static properties, you wouldn't have to think about dynamics. These were basically classical models that people were thinking about. Even if you were thinking about the transition in a superfluid, you could map it onto a classical model of spins. The question was, how you'd solve a classical statistical model with a very large number of degrees of freedom at a point where you're starting to get diverging fluctuations. And there was a lot of experimental and theoretical work on that.

Zierler:

How--

Halperin:

Now, at the same time, it was realized that there were other properties like dynamic properties that were more complicated. Like you could ask, suppose you have a fluctuation in the spins at some wavelength, how fast does it relax as a function of time? Now you really need time-dependence. Then you have to ask what's the microscopic mechanism for production the relaxations? The Ising model would have none. If you have a Heisenberg model, (there's a quantum version and a classical version), there are dynamic mechanisms. And the question is, could you say something about this? And as I think I've already hinted, it was already partly understood: people had done sort of approximate mean-field type calculations. They all suggested that time slowed down; as these fluctuations got large in scale and magnitude at longer wavelengths, they couldn't happen very fast. You wouldn't be able to heal them very fast, so timescales would slow down. And there was something called the idea of critical slowing down, that if you measured fluctuations of various kinds and the time scale for their relaxation, they would tend to get slower in some way or other as you got close to the critical point. But exactly how that would happen wasn't at all clear. And that was the question that we got interested in, I think, you know, Pierre Hohenberg was really the one who inspired me to think about it.

He got interested in this by reading some papers on fluctuations in helium. And there were some crude ideas floating around that we heard about that caused us to think about it, and ask the idea to try to understand to what extent could you extend the ideas of scaling to dynamic properties, too. Dynamic properties -- these things are really dependent on time in an important way. We were still only thinking about classical models, we didn't think about quantum models, and to the extent that we might've thought about quantum models, we said, well since we're looking effects of long wavelength fluctuations, which are at very small frequencies, or very small compared to temperature over h-bar, quantum mechanics doesn't play a role. So the models we considered were all classical models, but they were still unsolved, and people didn't understand how to solve them.

And in doing that, we got interested in, we were inspired by some work on scaling by Ferrell and coworkers, beginning with work on helium. We were thinking about that and I remember, I think, that Pierre had a talk with Paul Martin, who had been his thesis advisor, you know, "What should we do?" And Paul had said, "Well, you'd be really more interesting if you think of other systems that this might apply to." And so we had sort of formulated an idea of this sort of general ideas of dynamic scaling and how there'd be a new exponent, which we called z, which related to frequency to the wavelength, frequency to the wave vector, and that would be characteristic of the dynamic system. And we realized that one of the systems that might be studied was magnetic systems. And we developed, sort of, a hydrodynamic theory of anti-ferromagnets and ferromagnets at finite temperature, which was inspired by the two-fluid picture of, theory of, superfluid helium that Landau and others had developed.

And the thing that was interesting there, in something like the Heisenberg model, where you have a continuous broken symmetry, what would you find? It was well-known that at zero temperature, if you solved these models and there was a broken symmetry, there's a "Goldstone" mode, so-called, (I'm not sure it had that name at the time), but there were magnons [spin-waves]. The low-energy excitations in a Heisenberg [ferro]magnet are magnons, which are exactly soluble, and they have a quadratic dispersion. In anti-ferromagnets, they have a linear dispersion. It's not exactly soluble-- the classical model is exactly soluble, but not the quantum model-- but you can show nonetheless in some approximation that there should be a linear spectrum at zero temperature. But what happens at finite temperature? At finite temperature, if you calculate the magnons, they start becoming damped. You find that they're not perfectly sharp. You would calculate corrections from one magnon scattering off many others.

And what we pointed out, which I don't think was completely appreciated, was that if you went to long-enough regimes, --there'd be a scattering length, and if you went to length scales very long compared to the scattering length of one spin wave scattering off another, -- you would get a re-normalized stiffness constant, renormalized susceptibility. You would again get a spectrum which was linear: the frequency would be linear in the wave vector. Omega goes as some constant c times k. And this velocity c would be given precisely as the square-root of a stiffness constant divided by a susceptibility, both of which could be calculated completely, in principle, as static quantities. But they affected the dynamics, just as in liquid helium, where you can calculate the sound velocities from stiffness constants and the thermodynamic properties -- You have to know things like the specific heat and the compressibility, thermo-expansion coefficient. In liquid helium, there's first sound and second sound, which are undamped at wavelengths that are long compared to the scattering lengths.

The scattering length diverges at zero temperature, but at finite temperatures, there's always a finite length scale. Above that, there's a damping, but the damping goes as k squared rather than k, so it's small. The damping is negligible in the limit of long wavelengths, even at finite temperatures. Just as in, well, sound in air. It has a linear velocity, which is perfectly well-defined at long wavelengths. But at short wavelengths, it becomes damped. That's hydrodynamics, where you start with this complicated system with an infinite number of degrees of freedom, and at long wavelengths, you have only a few degrees of freedom that are important, because all the other degrees of freedom relax quickly. They're determined by a few variables, like the density and momentum, and a few other slow variables. And so we worked this out for magnets.

And then, this was an important ingredient for trying to talk about what happens as you approach the critical point, and where the velocity goes to zero, the damping increases. How does it increase? What's the ratio between the damping and velocity, and what happens as you cross over into the behavior above the transition temperature, where you don't have spin waves anymore, but you have spin diffusion? What's the relation between the diffusion constant and the spin wave constant? Some of this had been talked about within mean-field-theory types of approximations earlier. Paul Martin had done some work on it, and told us about it, but this was the stuff we worked out. Part, originally, using scaling ideas. And then at this point, the Wilson-Fisher renormalization group had been invented for static quantities. They introduced an expansion in four-minus-epsilon dimensions, for calculating critical exponents for static quantities, and we said, well can we generalize this to dynamic quantities? Part of the important insight was just understanding what are the universality classes?

You know, we know that an Ising model should have different exponents than a Heisenberg model, even statically. But dynamically, you have a Heisenberg ferromagnet and a Heisenberg anti-ferromagnet, which in classical statistical mechanics have identical static properties that can be mapped into each other. They have the same exponents for static quantities, but dynamically they're very different. One of them has a quadratic spectrum, the other has a linear spectrum, and at the critical point, they behave very differently. So we understood, you know, what were some of the symmetries and commutation rules or Poisson-bracket rules that you had to take into account in order to understand how to divide systems up into different classes that would have the same exponents.

And then there was the question of how do you calculate these exponents? In some cases, you could relate them to static exponents. As you could, for example, in the Heisenberg model, because the velocity was related to static exponents. So, then that fixed this quantity z, the frequency scale. But in other cases, you couldn't. And there were in some of these more complicated things, which we worked on with Shang-Keng Ma and, later, Eric Siggia, who both were visitors at Bell Labs at one time or another. And they were also, both of them were mathematically far more skilled than I, or even than Pierre, but certainly much more than I. And they solved problems that I could never have even dreamed of trying to solve, because of keeping track- You know, I would have made 100 errors and they could do it without errors. But they also had insights, and we wrote a series of papers on trying to calculate what these exponents would be. And we also spoke a lot to people like Gunther Ahlers, who was an experimentalist, who did a lot of these dynamic and static experiments. He was very inspiring.

Zierler:

And how-- Bert, how much was your work at Bell Labs, were you operating in an island at Bell Labs? I mean, how integrated were you to the broader physics communities? Were you presenting at conferences, were you in discussions with your colleagues in academia? Yeah?

Halperin:

Oh absolutely, yeah. I went to conferences all the time. I went to my first Gordon Conference -- I gave a talk at a Gordon conference, I think, when I was just out of graduate school. Mel Lax was chairman of the conference, and he arranged for me to talk there. That was, I think, in the summer of '65. And I went to conferences, sure, and presented. I went a conference in Japan in '68, where I talked about these scaling ideas. And smaller conferences. Definitely. And I went and gave talks at universities. We were very much connected to the outside world. The question is, other people at Bell Labs? Well, there were more-- I think there were more experimentalists than theorists working on critical phenomena there. But of course, I was also working on many other projects with other people on other subjects, but--

Zierler:

Did you ever feel pressure to monetize your research? That it needed to be able to be profitable to Bell Labs?

Halperin:

Absolutely not.

Zierler:

Yeah.

Halperin:

No, but I didn't have my ears to the ground at that time. I was there for three years before I even realized there was a merit review process going on. That's how dumb I was. I was interested in physics, and I didn't think about getting ahead. But then later, you know, I sort of asked, "Why are you guys paying us?" You know, when I started thinking about it, you know, what's go--

Zierler:

Right. Uh-oh. (musical notes sound)

Halperin:

I was in Department, in group, 11111, which was the most abstract. Well, there were also math groups that were more abstract. But a certain number of people were employed to be there as consultants to talk to people who were doing more applied things, and undoubtedly for prestige purposes. And what they wanted from me was to write Phys Rev. Letters. As long I was I doing things that were recognized by my colleagues as being important, they were happy. That's what I later learned about the [merit] review. I think that's what they had to talk about-- the number of Phys Rev Letters and how you were regarded in the outside world. And that's what they were interested in for one reason or another. Partly for prestige, it helped them attract people who were doing more practical things, and it might help them if they got into trouble. So what happened in the early 70s when they were falling behind-- other places started making integrated circuits, and Bell Labs, the inventor of the transistor, wasn't able to do them? Then they started really being, looking at the bottom dollar, and there was inflation going on. And a lot of people were pressured to drop what they were doing on particular experiments and start working on silicon. But it didn't extend to people who were as far out as I, very--

Zierler:

Ah, Bert, we cut out again. I'm not sure if you could hear me.

Halperin:

--Okay.

Zierler:

Oh, you're back. There you go. So the last I heard, you were saying that as a theorist, you were too far out for those bottom dollar issues to ever feel like they affected you.

Halperin:

Yeah. I mean, they did in terms of the long run, I certainly worried about the long run- It caused me more to worry about the long run of future at Bell Laboratories.

Zierler:

Right.

Halperin:

There were other things like anti-trust suits and so forth going on that also--

Zierler:

So even as early as the early-mid-1970s, you sort of saw the writing on the wall in that regard?

Halperin:

I wouldn't say I saw the writing on the wall, but I had worries, you know. Writing on the wall, no. But I had worries about maybe things would sour, and that we weren't really doing any-- that I wasn't really doing anything useful -- and if times got tougher, Bell Labs might not always continue. I remember even, this was maybe later, when I had my second offer from Harvard, I spoke to Phil Anderson about it. And he said, well, he didn't really understand either why they were supporting us, but…

Zierler:

(laughs) It's a good thing.

Halperin:

Yeah. But it was a good thing, right. So that was my, yeah. I wouldn't say I saw the writing on the wall, but I had at least enough presence of mind to know that it might not continue another 40 years.

Zierler:

Right.

Halperin:

Of course, the universities weren't in great shape either, in that, but I knew that a place like Harvard would continue. It had been around for--

Zierler:

Sure.

Halperin:

For long enough that I knew it would continue. I didn't know whether I would get research support. I certainly didn't know that research support would continue, but I knew that at least I would have a job and there'd be interesting things to do: teaching. I enjoyed teaching, I liked teaching, but it was a lot of work, I’d found.

Zierler:

Yeah. So how did your second offer with Harvard come together? Did you reach out to them—?

Halperin:

No.

Zierler:

Or they recruited you again?

Halperin:

No, no, it was Paul Martin. Paul Martin was courting me all the time, and okay, so there was a... They had, after I turned them down the first time, they hired an assistant professor, Alan Luther, who had done some nice things, and he was up for tenure, but they had this policy of looking all over the world first. There was going to be, eventually, an ad hoc committee, but first they had to do a search to find who was really, they thought, was best. And Alan was in competition with everyone else. And Paul Martin asked me if I would be willing to be considered. And I said, "Well, yes." And this would have been maybe spring of '75 or something like that. I said, "Well, I don't know." So anyway, since I didn't say absolutely no, they put me in, and I guess the department voted to make the offer first to me, or there was an ad hoc committee that decided that I should be the number one candidate. I think if I had turned them down, they might have promoted Alan, I don't know. Anyway, at the time, I was very torn. And--

Zierler:

What kind of assurances did you get that you would have research support at Harvard?

Halperin:

Well, okay. So, Paul Martin told me that it really wasn't much of problem. He and Henry Ehrenreich had a group grant, and there may have been, may have been an assistant professor on it as well. And they could, at the beginning, they would take me in, I could join them, and so I would have money to pay for a student, and they would apply for more money for the grant, and they were reasonably confident that it would come, and, of course, things were tight, but they weren't that tight. And a lot of students came to Harvard with their own money like NSF fellowships and so forth. And the research could go on even without grants, but things were tight but not that tight. And I wasn't planning on having a really big group. I didn't have an experimental lab to run. So, even if I had no research money at all, I could still do research.

Zierler:

Right. You mentioned earlier, for I think it was for your first offer, that you were concerned that maybe you didn't have enough ideas to keep graduate students busy. I assume over the course of your time at Bell that that concern faded away? You did have ideas for graduate students.

Halperin:

Well it became less, I would say. It was always an issue, you know. You're always worried about whether or in not you have enough ideas, you have enough good ideas. The ideas you have, the good ideas, are harder to come by, and so yes, it's always a problem. But I was, had certainly more self-confidence after five more years, yeah.

Zierler:

And in committing--

Halperin:

So they made the offer in '75, and eventually I said I would come in a year. I didn't want to leave immediately. it was getting late and I deferred for a year. That's what happened. So I came in '76.

Zierler:

And in thinking of your game plan for, you know, getting to Harvard, are you thinking that you're gonna try to make the research as seamless as possible, or is this new opportunity, new environment, you're gonna do new projects?

Halperin:

I was always looking for new projects, but I certainly expected I would continue stuff I started with, if I had to put students on something. I certainly intended to continue many of the things I'd already started, but I certainly expected that there would be new things coming. I didn't know what they were going to be. It wasn't that I had a specific thing I was going to Harvard to work on. I just said, "Well, this is a good place. They're good people who will attract good post docs." I had a lot of respect for Paul Martin, for Henry Ehrenreich. I knew that they would be good people to talk to and that there'd be good students and lots of seminars, and that if you wanted to do state-of -the art condensed matter, (at that time it was called solid state physics), Harvard would be a good place to do it for a long time to come.

Zierler:

And you came on, did they bring you on as a full professor?

Halperin:

Yeah. At that time, that was the only tenured position. Some time earlier, shortly before that, they had made the associate professor position non-tenured; there were no more tenured associate professors.

Zierler:

Right.

Halperin:

So there were only full professors… Unlike most other universities, at Harvard, only full professors were tenured.

Zierler:

And was it at Harvard that you first got interested in quantum Hall effects, or you were doing some of that at Bell Labs?

Halperin:

No, no, it hadn't even been discovered until 1980. Although, well, let's say what's now known: There was, certainly, in 1975, there was work in Japan, theoretical work which anticipated it. It hasn't gotten proper credit, but there were also experiments that looked at two-dimensional electron systems in strong magnetic fields in semiconductors. And they noticed plateaus and stuff, but they didn't know how accurate they were, and they were more interested in, the focus at that time was, much more in what happened when the Fermi level was in the middle of Landeau level, where you didn't have a Hall plateau and you had a finite resistance. They were interested in what is the value of the resistance under those conditions. That was something that I might have been vaguely aware of, but not much. It wasn't that exciting, and it wasn't the focus of a lot of attention until the experiment of von Klitzing in 1980, where he saw these plateaus which were accurate to part in ten to the sixth. The Hall conductance was given by an integer times e squared over h. And with different integers on different plateaus, but agreeing with each other to a part in ten to the fifth, or ten to the sixth. It was unprecedented in any, in just about anything, in condensed matter.

Zierler:

And this is what piqued your interest in getting involved in this research?

Halperin:

How?

Zierler:

And this is what piqued your interest in getting involved in this research?

Halperin:

Oh okay, I've told this story before. That I didn't know anything about it. This paper was published in 1980, I was not aware of it. My awareness came in 1981, when I got a call from Gloria Lupkin, who was then maybe chief editor, or an editor, at Physics Today. And she was interested in doing a story. She had heard that some young guy at Bell Labs named Bob Laughlin had come up with a theory to explain these plateaus and why they were accurate. And to explain the quantum Hall effect. And she had heard about this, it wasn't published, but she had maybe heard about it from Phil Anderson, who had heard it from Bob. She thought it was maybe interesting, so she wanted to know, did I know about? She had already known about me from other things, and we had a collegial relationship. So I said, "Quantum Hall effect? Never heard of it. What is it?" And she told me about it, and I said, "That's really interesting." And then I learned about Laughlin's theory in detail, I can't remember whether I learned more about it from her or from him, or from someone else. I gradually learned about it, I think, before it was published, maybe. Or maybe I saw a preprint. And I realized that this was really a brilliant insight, and that the whole subject seemed really interesting. And his paper, although it was brilliant, wasn't that easy to understand, and it raised some important questions in my mind, which I got interested in.

And that's how I got personally involved, trying to clarify his paper, and I realized that it implied some things that were counter-intuitive, like states that didn't get localized by disorder in two dimensions, and even one dimension, which was contrary to the folklore at the time. These one-dimensional states, which in the end, had been predicted, if you look back at stuff, were the quantum analog of classical skipping orbits, consistent with the fact that they'd be one-dimensional states that that moved in only one direction around the Landau level. Essentially they had been predicted by Azbel, many years before. But in a different context, a three-dimensional context, and the importance of them was not so great there. So I didn't know about all this stuff, but anyway, that was what got my interest. And it turned out that I wrote a paper explaining this, which turned out to be influential, although at the time, I didn’t think it would be. I remember that Laughlin didn’t publish his explanation in Phys Rev Letters; somehow it got published in Phys Rev Rapid Communications, or something. So I didn't submit my paper to Phys Rev Letters, out of respect for Laughlin, because I thought he had the basic idea, although in fact it turned out to be one of my most referred-to papers. So, it was published in Phys.Rev., as a Rapid Communication, I believe. I didn't appreciate it as being that important at the time.

Zierler:

And why was it? What was the long term, I mean what was the effect of this paper in the field?

Halperin:

Well, I think the answer is the fact that it led to the understanding that if you really wanted to understand what was going on in experiments on quantum Hall effects, you were always making contacts to the edges, and the way the edge states behave becomes important. And then when people talked about fractional quantum Hall effect, it became even more important. So the focus on edge states has become important. The fact that edge states have very interesting properties became important in the context of fractional quantum effects. More recently, when people talk about topological insulators in two dimensions and three dimensions, a lot of them are like the quantum Hall system in some sense. They have an energy gap in the bulk, so the bulk is a little hard, often, to distinguish from an ordinary bulk, but they have peculiar properties on the surface, they always have gapless edge states. For example, there is a two-dimensional topological insulator without broken time-reversal symmetry, which is sometimes called the quantum spin-Hall effect. A two-dimensional topological insulator in zero magnetic field has no obvious properties in the bulk that you can easily measure, but it always has low-lying edge states, gapless edge states, and there are consequences of that, for example if you make electrical contacts to the edges. So again, the focus on edge states has turned out to be really important, way beyond the quantum Hall effect. But I can't claim any insight for that. Yeah, it's luck that something you do turns out to be more important than you expect.

Zierler:

Now, your work on quantized Hall states and unquantized Hall effects, was this happening at the same time, or this is sequential?

Halperin:

Oh no. The unquantized Hall effect was much later. So that's a paper that I wrote, I wrote it actually in 1992, while I was on sabbatical, I was partly at Bell Labs. But it was published in '93. And this was 10 years after the discovery of the fractional quantum Hall effect. It was very, very different. And no one even focused on that problem at that time. People didn't really think it was all that interesting. What they’d found was that you had plateaus at odd-denominator fractions and not at even-denominator fraction. In general, not at even-denominator fractions, and it was understood by at least, 1989, with Jain's work and so forth, why the odd denominated fractions were what they were. Which ones were the prominent ones, why they were different.

One of the things I did show in 1983 or 4 was that at least in principle, you could have even denominator plateaus. Quantized plateaus. But I didn't know how to do it in practice. I just said that there's no fundamental reason it could not occur. I could make a crazy model that would do it, but not a realistic one. Then these were discovered in around 1987, like at filling fraction five-halves, there were plateaus. But at filling fraction one-half, it just looked like nothing interesting was happening, and people didn't pay much attention to it until 1990 or so when there started to be experiments that showed that there were interesting things happening. And then, around that period, 1990, we started getting interested in it. It took two years before we actually had a paper to write up, because there were a lot of things to be done. But it was at least 10 years later than 1980 that people focused on, well, it's not so trivial what's happening at filling fraction ½: even though there's not quantum Hall plateau, there are other interesting things happening at this filling fraction one-half, where a plateau at one-half e-squared over h is not seen.

Zierler:

Uh-huh. And was the impact of this work more in the theoretical end, or the experimental end? Or both?

Halperin:

Which?

Zierler:

All of the work that you were doing in this area.

Halperin:

Well, it was certainly, I think, both. There were both theory and experimental consequences. I mean, I was always more interested in... Maybe it was part of my Bell Labs influence, that there was a high premium on explaining experiments, rather than on pure mathematical proofs. Although, I always enjoyed, some of the things I liked best, were clever mathematics. So, you know, the first paper I wrote that I was very proud of, had no relation to experiments whatsoever. But most of the things we were interested in, certainly in dynamic critical phenomena, we were very much interested in experiments. Quantum Hall effect was certainly motivated by experiment. That was something where, again, the experiments were ahead of the theory. They motivated the theory, and we were trying to understand what was going on, and make predictions for what would happen under other circumstances, and explain data, so that's always been certainly my focus, and a lot of what I've gotten most pleasure out of is explaining experimental mysteries. Sometimes small ones, not necessarily big picture things, but small things, like an experimentalist comes along with something they really can't understand, and then maybe I've got a clever idea, I'd understand it. And that gave me as much excitement at the time as some of these bigger-picture ideas, like the edge states and so forth.

Zierler:

And when did you get involved in one-dimensional systems research?

Halperin:

Well, of course, part of my thesis was in one dimension. But at the time, I thought, well, that was just because I couldn't solve the problem in three dimensions, and a real man wouldn't work much in one dimension. I was pressured into writing a review article on one-dimensional systems, but I didn't think there was anything very interesting about them. I thought they were just something you could solve mathematically. Only much later did I realize that they really had unique properties that were different, that whereas with three-dimensional systems, sort of looked like non-interacting systems, one-dimensional systems really were different. Because once you put interactions in… what I didn't understand was, once you put interactions in, it really made things different. Although there were people at the time like Elliot Lieb and so forth who certainly understood this, Lieb and Mattis. But I didn't, and so I only really got more interested in them when I started looking at fluctuations in superconductors, the stuff I did with Paul Martin. We got interested in two-dimensional superconductors, but also one-dimensional superconductors and superfluids. And then I wound up as a collaborator on a paper with a bunch of people at Bell Laboratories on one-dimensional metals, but I wasn't a major player in it.

And then I got... Let's see, so there were several one-dimensional problems I got really interested in much later. That would have been... There were several papers on spin systems that I got interested in through speaking with Ian Affleck, after I was at Harvard for many years, and then this work on one-dimensional electron systems, which I got interested in partly through the work of, experiments of, Amir Yacoby, who is now my frequent collaborator. At that time, he was a visitor at Harvard, and he had some very puzzling experimental data that we were able to explain, and that got me really interested in the system more broadly. So it's been not some kind of, "Oh, I think one-dimensional systems are what I should work on." It's just that, well, here were some really puzzling problems that happened to do with one dimension. So I had to learn about one-dimensional systems, and I learned that they were different from two-dimensional systems, when the interactions were present in interesting ways, and that's the way it worked.

Zierler:

And what about your involvement in mesoscopic systems? When did that start?

Halperin:

Well, certainly a major incentive was trying to explain experiments that were done by colleagues. So, Bob Westerfield was doing experiments on mesoscopic systems, that I found quite interesting in, that would have been, around 1980-ish. And later, I got interested in experiments that were done by Charlie Marcus, who was at Stanford, but then later came to Harvard, (and I was sort of instrumental in bringing him to Harvard at the time). And I was interested in his experiments in mesoscopic systems. And then Amir Yacoby came to Harvard and did experiments and experiment on said systems. At one point, under Charlie's leadership, while he was still at Harvard, they got a big grant, a multi-institutional grant from DARPA, to investigate, to try to make spin qubits in gallium arsenide quantum dots. And they had a lot of experiments, interesting experiments, going on there, and they brought me in as a theorist. So I got some research money out of it. I was a co-PI, and, well, once I was involved, that helped. I was interested anyway, but this, if you wish, helped to cement my interest. And we worked together. They did a lot of interesting experiments. I don't know that there's ever going to be a quantum computer based on gallium arsenide qubits, but we learned a lot about spin, electron spins, how they interact with nuclei, how they relax. Among other things, Amir had some beautiful experiments to create dynamic nuclear polarization using them, and then using these polarized nuclei to manipulate the electrons in ways that he wanted to do for quantum computing. And so I found it intellectually very interesting. Although I can't say that I'm a great believer in quantum computation, but I find the problem, intellectually, extremely interesting.

Zierler:

Well, Bert, I wanna now ask you some sort of broader questions that might get you to reflect sort of more broadly on you career--

Halperin:

Let me just get a, I need a drink of water. Let me just--

Zierler:

Sure. Take your time. So I want to ask you about, thinking about the hands-off approach of your thesis advisor, I want to ask you if you could reflect on your style as a mentor for you students, and, you know, the ways that you encourage them, the ways that you sort of let them work out problems on their own, when you decided to step in and help them. Do you have sort of general principles that you apply for mentorship of your students?

Halperin:

Well, so I think I was influenced by Hopfield. He once pointed it out to me much later, that he was aware that he was sort of a hands-off kind of guy. He wasn't sure that was the best way, and he wondered if it had influence on me. And I could see that, later on, when I saw younger people come in who were much more, you know, had a more group-type approach, worked more closely with a group. It’s not that I only worked individually, I often tried to put a post doc and a student together, and so forth. So I certainly did that, but I was not someone to come and ask them every week what they were doing. I didn't have group meetings where I tried to keep up on things. In retrospect, I think that was probably not so good. Probably I should have been more hands-on, and I suppose this might have come partly from Hopfield, but again, it suited my personality. I was happy to work by myself. Maybe Hopfield might have worked more with other students, I don't know, but so... I would say that, I mean, certainly, I've had students that I've worked pretty closely with on their projects, but again, it would typically be, I'd see them only once a couple of weeks to ask them how they were doing, or when they would come by. And I'm not sure that's the best way of doing it. Again, it depends on the personality of the thesis advisor. I tend not to be such a social person. I mean, I enjoy... I'm not anti-social, but I'm not as person-oriented as I see some of my colleagues are.

Zierler:

In thinking about the achievements of your students, are there any that really stick out as making you the most proud?

Halperin:

Well, okay, so I had a number of very good students. Certainly, I would say, Daniel Fisher was one of my best students. He's done beautiful work. I can't say that I had a lot of influence on him. He was pretty independent. He was also worked with David Nelson as well, who was a post doc at the time. I had some projects with Daniel that I was very pleased with and enjoyed working with him, but I don't know that I could say that I set much of an example, I don't take credit for his success. He was brilliant when he came, and he was brilliant when he left, and he was very good. I've had a number of other very good students. Partha Mitra, Steve Simon. I could mention many of them. I had a student Shechao Feng who was very good, but unfortunately died at a young age. And various other-- A lot of students who've done very well, gotten quite prominent positions at universities. I don't want to go through the whole list of mentioning the ones that did very well. Cathy Kallin did very well, in Canada. And Yaroslav Tserkovnyak. Yeah, I don't want to go through them, because I don't want to leave out… I'd probably be leaving out too many that are good. And the extent to which I can see my influence on them, it's a little hard to see sometimes. They'll claim that I influenced them, they'll give me credit, but I'm not sure. If students are really good, they are really good, so..

Zierler:

Yeah. In, you said before that, you know, you're always searching for the next--

Halperin:

Chris Henley is one that I think I really should mention. He was really brilliant, and he went to Cornell, and did some brilliant stuff at Cornell. He unfortunately passed away relatively young; he was 59 or something when he died, but he's a loss. So I've lost a number of my students and also some post docs. Of course, I have had many very good post docs.

Zierler:

I want to ask you about your decision-making process when you decide to pursue a new inquiry, a new area of research. Is there always... is there something that, when you make that decision, that's always shared? Is it an intellectual curiosity? Is it a desire to advance the field? Are you thinking about applicability? What's your, I mean, if there are general principles that you would apply to every decision about whether to take on a new project or not, what might those principles be if you have any?

Halperin:

No, I don't. I mean, if it interests me, I try to think about it. I would say that my desire has been rather quantitative. I like to feel that we should have a quantitative understanding of things. And my original involvement in physics was certainly coming in from math, and I originally thought about it as an applied math area. As I got more and more involved in experiments, I got more and more thinking about it in terms of experiments, but I've typically have been attracted to problems where I think there should be a quantitative answer, and they don't understand what's going on, rather than saying, "We don't understand anything and we should start a whole new field." Like de Gennes who said we we really don't understand anything about liquid crystals, and he started a whole new field. I have not had that kind of inspiration, unfortunately, so typically, I have been attracted to things that we half-understand but not quite. That is not necessarily the best way to do physics, but it's the things that have interested me a lot, and it may be part of the reason why I relatively early bowed out of the high-temperature superconductivity game. I was interested originally, but when I decided it was really very complicated and one had to digest a tremendous number of experiments and things, a lot of things were going on, I felt I didn't have that much that I could contribute to it. I felt what I could best do is try to think about a problem that needs to be clarified, where we partially understand what's going on, but not nearly as well as we should. Now that doesn't mean that it doesn't lead to new things that you haven't thought of. They may come out of it, but what, it's not where I started from usually.

Zierler:

Do you operate better working on multiple projects at the same time, or do you try to do a sequential approach?

Halperin:

I would say that I have, you know, over the course of a year, I would be working on several projects, certainly, but, in a given week, I might concentrate on one problem. It's easier for me to do that now that I don't have students. When you have students, if they have several different problems, you have to think about all of them a bit, but that was not necessarily... I didn't necessarily succeed in it all that well. And so I do in any given day tend to think about one problem. Get focused on a problem.

Zierler:

It's an interesting framework you brought up, that you tend to, you're attracted by problems that are half-understood, and you want to sort of complete the understanding. So by that metric, do you tend to stay on a project until it's understood? Or do you feel like at some point, you need to jump ship and just move onto the next thing?

Halperin:

No, I certainly, I do often work on a problem and I get tired. If I'm not making progress on it, I will give it up—

Zierler:

Right.

Halperin:

-go with something else and maybe come back a year later or two years later.

Zierler:

And what's the feedback mechanism? How do you quantify and also qualify, what does making progress mean? How do you know if you're making progress? How do you know if you're sort of hitting a wall? How do you determine those things?

Halperin:

Mmm. I don't know, usually it's kind of obvious if you're just thinking the same things over and over again and not getting any further in understanding what's going on, or if you say, "Oh, here's a model." And I solve it. Uh-oh, it doesn't work. But sometimes it's a little harder to say, have I made progress or not. And if I feel I've gotten more understanding, even though I see what I did was wrong and I made various errors of assumptions, I might feel that, well, at least I've learned something from it. And I'll continue now. How long I'll continue depends a little bit on how important I think the problem is. Whether there are other people involved, or if I'm alone. If I'm working with other people, sometimes that's an incentive to keep going. Because they're involved in it. And certainly, if it's a problem with experimentalists, that they're doing the experiments anyway, it tends to keep my nose to the problem a little bit more. And then having discussions. Sometimes, you hit a dead wall, and if you have collaborators, they may get you over the dead wall, or they'll point you in a different direction. Certainly, experimentalists may tell me something I don't know. So--

Zierler:

And do you have a formalized approach to determining the relative importance of a given problem? Or is it basically just an intuition? I mean, how do you know when you say, you know, this problem is important because of X? How do you determine importance in the problems you work on?

Halperin:

Let me get the light a little better here.

Zierler:

Is it the impact that you see that this will have on the field? Is it simply how curious you are on the situation? How do you define importance as a way of motivating yourself to either stay on it or not?

Halperin:

Well, I think importance would be…. As I say, I'm not only motivated by importance. I'm motivated by curiosity for various reasons. I want to understand it. Importance, I would say yes, will it attract attention in the field? Will it be referred to? Will it change the way people think, either in the short run or maybe not now, but maybe I can see that when experiments get better, sometime in the future, it will have an influence. So that's certainly the way I would define importance. The extent to which I can properly evaluate them, that's another matter. You know, there are things that I don't think are necessarily that important, but I often don't anticipate how important something will be. Certainly, if I think something is important, it will be a strong additional motivation to try to solve the problem. But it's only, in my case, only one of things that I take into account.

Zierler:

On the question of understanding, what's an example, or several examples, if you want, of things that you understand now that you didn't understand at the beginning of your career?

Halperin:

Wow. Almost everything. I don't know. A lot of things have been discovered since then, but... Yeah, I've had a long career, so. (laughs)

Zierler:

I'm asking broadly. Like, not just for you, but in condensed matter physics, solid state physics. Things that were mysterious at the beginning of your career where either your field or you personally, you know, really moved the ball forward and there's real, fundamental understanding now in a way that there wasn't at the beginning of your career.

Halperin:

Well, certainly critical phenomena is something that wasn't understood. And not just dynamic critical phenomena. But critical phenomena is now pretty well-understood, although there certainly are open questions. I just learned very recently, it turns out that there have been some beautiful new bootstrap calculations that set very rigorous bounds on the exponent for the correlation length exponents in, basically, in the superfluid transition of liquid helium. It's the O(2) model in three dimensions, which is the university class that liquid helium should fall in, and they have predictions now, something like six decimal places or something like that, or more. And there are experiments that were done in the space shuttle which claim to have results, which they also have to six decimal places, and they disagree in the fourth decimal place. And which is ten times more, or eight times more, than the quoted uncertainties in the experiments. What's going on there? I don't know. So maybe if that part, if that's wrong, then we really don't understand what's going on. That's really hard to imagine that we didn't get that right. So there are still things that are still not understood, even there. Let alone values of critical exponents in the gas liquid transition and so forth. There are a lot of things that are not so well-understood, but they're not the focus of that much current interest. But any case, that's certainly by and large something that was not understood in 1965, and is largely understood now.

High temperature superconductivity wasn't even imagined, and it's largely still not understood now, although some people think they understand it.

The quantum Hall effects hadn't been discovered, and well, quantum Hall effect is not one thing, it's a whole field, you know, lots of different phenomena that fall within this general category of two-dimensional electron systems in strong magnetic fields. Integral, fractional quantum Hall effect, what I called the unquantized quantum Hall effect, etc. Many other things, which are at some level understood, although there are certainly many cases where you don't understand why some particular material shows a fraction and this one doesn't. Or, what's going on in this five-halves state where they do see a plateau. What's going on there, people thought they understood that back in the late 1990s. It was thought that that was understood, and now there are recent experiments that were done in Moty Heiblum's group that throw a monkey wrench into that, which people really don't understand. They're beautiful experiments that seem to be getting results that contradict what everyone thought should happen, and we don't understand why. So these are definitely open things that are very interesting. There are a lot of interesting problems in quantum Hall area that still interest me, for sure. These were things that were not all understood, because they didn't even know they existed.

Zierler:

Right, right.

Halperin:

Things, superconductivity was, okay, by 1958. That was, by the time I came on the scene, that was more or less understood. But there are a lot of things that happen on surfaces and a lot of materials, certainly, that are much better understood now. People understand much better how to compute properties of materials, for example, which is very important. I mean, solid state physics supposed to be able to do that. We're supposed to be able to understand what happens in the real world under all kinds of situations.

Zierler:

Yeah. On the question of the quote-unquote "real world," do you concern yourself with the extent to which your research has translated to practical applications? is that something that is interesting to you, or do you not really care much about that?

Halperin:

Oh, I'm interested, and I'd love to know that something I did had practical consequences. I'm not sure that any of it has. It is not been the primary motivating feature, but I mean, many people, fortunately, are motivated by, you know, what can really help the world, or help industry, or something. And at times I've looked at a few things like that, but I never saw anything... I never found anything where I felt I could make a real contribution. I've worked on some projects with people who did have that as a longer-term goal, but I never felt that my contribution to their understanding… Let's say, indirectly, I felt that if I helped them understand what's going on, it may help them do more practical things. But that's the extent of my being able to justify what I've done for the real world. [And, of course, many of my students, and students that I have taught in classes, have gone on to work on practical applications.]

Zierler:

So that's to say, then, that the pursuit of advancing knowledge is, in and of itself, all the value that you ever were interested in creating?

Halperin:

No, I wouldn't say that. I would say it's all I've succeeded in creating. And it's, I haven't made a concerted effort. I wouldn't say I wasn't interested. I would have been interested, if something, if I saw-- I mean, I've certainly been interested in practical things as a spectator. I'm certainly interested in it, and I'm definitely interested in it, as any scientist would be, as a citizen. But not something that I've really said, "Well, here's something that if I spent six months on, I could really have an impact on. And unless I saw that I could have some impact, or six months, or whatever, unless I saw that I had some probability of having an impact on it, it doesn't act as much of an incentive to me. That's what I would say.

Zierler:

Over the course of your career, how has respect for science and scientists changed? Over the many decades of your career, if you could roughly draw a picture of the way science is regarded in society at large. Are there high points and low points?

Halperin:

I'm a poor person to ask, because I'm not on the-- I'm only barely in the 21st century, in some sense. I mean, I use the internet, I certainly use the internet, but I still read newspapers, you know? I don't know. What do I know? I know what I read in newspapers. I live in Massachusetts, it's not really the United States. I hear about what's going on in the rest of the country, but I find it hard to believe. So I only know what I read. And I don't trust, necessarily, what I read. I think, you know, I've certainly gone through-- certainly, I would say, in the 60s, scientists were sometimes regarded as evil, but held as brilliant, and people listened to what they had to say. And maybe respect for physics-- physics hasn't played so much of a role, but biology, medicine, -- I think people do think that scientists are smart, but maybe they're evil or maybe they're good. The business of "fake news" and believing that scientists are lying and that global warming isn't real, all this is new to me, as far as I know. I read about it. I know it's happening. When did it happen? It certainly wasn't as prominent then, politicians weren't openly anti-science, certainly. I don't think it became a political football until more recently, that's certainly changed. There's certainly, I know that I was told at some point, I remember, it may have been the 1970s, I think I was already at Harvard, that they were like ten times as many astrologers in the country as there are astronomers. Okay, so, you know, that sort of thing is not new. That people had mystical ideas of relation between the stars and their futures. You know, things that to me didn't seem to make any sense, but I don't know that that's increased or decreased. But the idea that the news media were deliberately giving us false information, or that scientists were conspiring to mislead the country and undermine the economy? That I don't recall.

Zierler:

Yeah. Well, Bert, I wanna ask you I think one final question. it's a forward-looking question, and that is, what excites you about the future in your field, in your own career, in things that remain to be discovered, but that, you know, really might be discovered in the relatively near future? What are the things that continue to motivate you to be active in the field? And what do you hope to accomplish yourself in your field?

Halperin:

Well, what I hope to accomplish is different. I don't have a gang of students, I'm not able to really contribute to the forefront in a way. My role at this point is to try to explain puzzles. Experimental puzzles really interest me, and I get a lot of pleasure out of working with experimentalists and trying to explain things. If I think back over my career, to some of the things that I've done that have given me the most pleasure, not the most important ones by any means, but being attracted to some experimental puzzle, and being able to figure out something really surprising, that happened. It may have been an experiment that's hardly cited, that didn’t, in the end, have that much impact, but it was a correct experiment, and I could explain it. Those are things that have given me great pleasure, and they still do. As to where I can look at where the most active intellectual areas are, I could talk about things like topological classification of the different kinds of quantum states you can have. In general, trying to understand strongly-interacting systems: quantum Hall systems, fractional quantum Hall systems are an example, but they're a sort of relatively simple example, and it's one where you can do beautiful experiments on.

There are other systems that are more complicated, so it's harder to do experiments, but there are spin glasses and, of course, high temperature superconductivity, and the normal state of high temperature superconductors. These are all things that I think are really important intellectual problems. I don't see myself, well, okay, I could imagine making some contribution to the classification of topological insulators and stuff, and I speak to colleagues about it a bit, but I'm not, I don't know nearly as much about it as my younger colleagues. And they have groups of exciting post docs to work on it, and so it's hard for me to contribute. And they have better mathematical training. So I think it's exciting, but not something that I see myself doing. Obviously, I think just developing new materials is, from an experimental point of view, is very exciting. Among these, layered materials, including van-der-Waals bonded layered materials, and artificial materials of various kinds, certainly are interesting. I think there are going to be surprises. I believe there'll be surprises that'll be very exciting, But I don't know what they will be, obviously, or they wouldn't be surprises. Mathematical techniques-- I'm impressed with some of the beautiful mathematical techniques that people have come up with for solving many-body-type models, such as the density-matrix renormalization group, and this or that generalization. You know, various things that I only partially understand. I don't understand well enough to be able to apply them. Let alone that in order to apply them, you not only have to understand them, you have to have good up-to-date computer skills, whereas I still know-- I learned Fortran back in (both laugh) 1960, and I'm not that much more advanced than that. And you need to have groups of students who propagate the information. You can't do it by yourself. So, these are a lot of these things that I see as the future, or the near future. I can't say what the far future is. But these next-20-years type of things are things that I would be happy to try to recruit people to Harvard to do. But I'm not expecting that I will personally make that much contribution.

There's a lot of excitement about relaxation to equilibrium, and behavior of quantum systems far from equilibrium that are isolated systems. Things like many-body localization and so forth, and entanglement issues, possible hardware for quantum computation, algorithms for quantum computation, and analyses of. what quantum units could, in principle, do, which I think are very interesting intellectually. Whether they will have any practical application, whether any of these things will have practical applications, I’m not so sure. But again, I don't feel that I'm really able to have a big impact. It's all that I can do to try to understand what's going on, but it certainly interests me.

Zierler:

Well, Professor Halperin, I wanna thank you so much for your time today. It's been really amazing talking with you. I really appreciate it.

Halperin:

Well thank you, David, it's been great speaking with you, and good luck.

Zierler:

Okay.