Physics of Scale Activities

Kadanoff interview, part I
 

Interview with Leo P. Kadanoff, 11 July 2002

Leo P. Kadanoff is John D. MacArthur Distinguished Service Professor Emeritus, Departments of Physics and Mathematics, University of Chicago.

Interview recorded in Chicago by PoS collaborators Babak Ashrafi, Karl Hall, and Sam Schweber.

Topical links within the interview:

I. Biography and training as a physicist

LPK

    I propose to spend five minutes telling you about my boyhood education, and we can go on from there. I was born on January 14, 1937, in New York city. My mother was a schoolteacher, my father an attorney. They were educated at Day and Night school, at New York University and Columbia. I went to standard grade schools in New York City, I grew up on a street which was notable for having many scientists within shouting distance. Roy Glauber, who eventually became my thesis adviser, grew up in the same apartment house that I did, at 110 Seaman Avenue, 204th street, as far west as you can get in Manhattan Island. Sheldon Glashow (Nobel Laureate, Harvard) was a half a block down the street. Gordon Baym (my co-author), about an equal distance.

PoS

    And you knew all these people as you grew up?

LPK

    I knew none of the people as a young man. I met them at Harvard somewhat later. I knew Glauber's family, and Glauber's family was one of the reasons I went to Harvard. After grade school education I went to DeWitt High School, an all-boys school about 5 miles away from home, I think because my mother did not want me to be too close to girls. There I was a reasonably successful high school student, went on at age 16 1/2 to Harvard University. By this time my family was reasonably prosperous, so I went on family money rather than on Harvard's money.

PoS

    In high school were you already clearly directed towards physics and math?

LPK

    I enjoyed physics and math, I took all the courses in many of the subjects that were available to me. I was a member of what was called, more or less, the biological setup crew, which set up the biological experiments. I took a couple of good advanced math courses from two teachers, both of whom had the last name Grossman, and were indecorously described as Fatty and Skinny, and I don't remember their first names. I got medium good grades, I was an excellent student, I was interested in science. I spent the summer working in the American Museum of Natural History in New York, writing numbers on human bones. It was my last non-remunerated summer -- must have been when I was 15 1/2. I was interested in mathematics, and read in it and enjoyed it, but didn't get much of a chance to do advanced things.

PoS

    What made you pick Harvard?

LPK

    I suspect it was my parents who picked Harvard. I think everyone thought it would be good, being an only child, somewhat spoiled, to be away from home, and it was pretty close, but not close enough so I could come home every weekend. New Haven would not have been quite far enough. First year at Harvard, I took math and physics courses. My parents wanted me to be a doctor. I enjoyed the physics course. I was not especially good at it, I don't think, but I enjoyed it enthusiastically and, following what was then the tradition, went as quickly as I could on to graduate courses in my second year at Harvard. I found the graduate courses an awful lot easier than the undergraduate courses.

PoS

    And this is the fall of 1955?

LPK

    I graduated from high school class of '53, so this would have been the fall of 1954 that I started to take an electrodynamics course from one of my future thesis advisers, Roy Glauber. The further I got in physics, the easier it got, as far as I could tell. I took the standard undergraduate courses, physics, mathematics, had a reasonably broad education at Harvard. Met my future first wife, decided that moving someplace else was too complicated, and went on to graduate school at Harvard. I was class of '57 as an undergraduate, so this brings me to graduate school starting in 1957. One of the major advantages I had partially because of the family connection, and partially for reasons that are not totally clear to me, I was part of the "in" group at Harvard by the time I was beginning graduate school. I lunched with Schwinger and his post-docs, and some of the other faculty people, and sat, I suppose, at the very end of the table, as the most junior person. But listened to what was going on, and was totally a member of the "in" group.

PoS

    When did you first meet Paul Martin?

LPK

    I must have met him in the course of my graduate studies. I do not remember the occasion. He was a young faculty member. You would probably be able to fill in the information better if you noted when he came to Harvard, since I was his third graduate student. Probably I did not meet him at the beginning of my stays at Harvard because he was not there.

PoS

    No, all I was trying to ask is, how did you become the "in" group with Schwinger, as an undergraduate?

LPK

    I don't know.

PoS

    You had taken his courses already as an undergraduate?

LPK

    I had taken his course already as an undergraduate. I hardly ever had a conversation with him until the very last year of my graduate trade.

PoS

    But you go to lunch with him.

LPK

    I would go to lunch with him, yes.

PoS

    The "in" group means that you had conversations with his graduate students and postdocs, and not with him?

LPK

    I certainly listened to the conversations as they occurred. Exactly how I added to them is not within my recollection. I was a brash, brash, brash young man, and would probably have said more than a wise person would have said.

PoS

    And the "in" group at that stage, Ken Johnson was still there?

LPK

    Kenny was still there. Paul Martin, Kurt Gottfried. I had heard discussions of his exile to Europe because he had the wrong kind of visa, and his return to Harvard. The group met at an Alsatian restaurant you probably know: Chez Dreyfus. They had a 99 cent special for lunch, and Schwinger had the $2 steak. You can see that my recollections are spotty at best.

PoS

    Who were you talking to a lot?

LPK

    I spent a lot of time with my fellow students as a graduate student. I remember a close family friend, Popat Patel, who became a nuclear physicist and went to McGill. There were other people, unconnected with physics, who were my acquaintances and friends in graduate school. Although my recollection is not tremendously good, I was probably self-sufficient. At some stage I got a problem from Roy Glauber and went off to work on that, and probably spent a lot of time with a pad of paper and a pencil.

PoS

    And it was always clear you were going to be a theorist?

LPK

    I never could figure out which way to turn a dial to achieve a given effect. I tell the story which maybe be apocryphal, that my partner, Jack Sanderson, in the lab course, told me to keep both my hands on the lab book. (laughter) But although the story might not be correct in detail, it's right in spirit.

PoS

    In your first year of graduate school, there's a choice to be taken, high-energy or...?

LPK

    It was never outlined to me that way. Because of the family connection, I started out with Roy. And Roy was interested in problems in the fundamentals of what you might describe as low-energy electrodynamics at the time. That part of my thesis was about an electron in a cavity and it's interaction with radiation. This was just before the invention of a coherent wave picture, and we didn't have the full mechanism that one uses to work on laser problems. But through the earlier work of [Sinitskii] and Schwinger, and then through the work of Glauber, we were talking about the non-linear effects in the interaction of light with electrons in a cavity, and that was the content of the thesis, although it was somewhat hard slogging. The best stuff came after, because of inventions and discoveries that come in after that.

PoS

    So when you come in to first-year graduate school, which would be the fall of 1957, Martin has come back, Martin and Schwinger is being written, or?

LPK

    Yes, and so you have to visualize we're taking this succession of core graduate courses from Martin and Schwinger and Glauber and other people, and I am listening to Schwinger's vision of how quantum mechanics should be thought about, I'm hearing from Glauber about his high-energy approximation, the eikonal approximation, and learning about the local work. However, I'm also noticing that there are a tremendous number of people who are chasing after a very limited amount of Julian's time. Whereas Glauber and Martin are more easily available to me, and it seems natural for me to be involved with them.

PoS

    How about your education in statistical physics or thermodynamics?

LPK

    I have mixed memories. I would have imagined that I'd taken a graduate course from either Glauber or Martin or both, but I don't remember that. I remember doing an oral examination on statistical things as the analogue of a candidacy exam, and I believe that in preparing that, I read many of the standard books on statistical mechanics, Tolman, and several of the other standard books. [Note added:] I did take a statistical mechanics graduate course from Glauber. It was excellent.

PoS

    Do you remember whether you picked up the second edition of Landau and Lifschitz, which came out in English in 1958?

LPK

    I'm embarassed to say that I have probably never read through any one of Landau and Lifschitz's volumes. I've used them, but I have never read any of them from cover to cover.

PoS

    But they're reference works, they're not--.

LPK

    --they're reference works, yes, and the quality of the index is such that it has cost me much pain (laughter).

PoS

    And your cohorts in terms of graduate students and talking to one another?

LPK

    I remember it was a lively business. On the other hand, the majority of the graduate students were housed in a room called B12, if my memory serves me correctly, at that time. I was not part of that, probably because of my personality, I did not have, as I recall, enemies among the graduate students, I was not part of it. I did have good occasional interactions with, for example, Popat Patel, whom I've already mentioned. I was probably to some reasonable extent a loner, and to some other reasonable extent absorbing the culture, not so much through the fellow graduate students, but through my lunchtable.

SS

    So your introduction to things like BCS, superconductivity, all of these things?

LPK

    BCS I can tell you about very specifically. Martin was interested in BCS, and perhaps a year and a half before I got my PhD (in September of 1960),he described to me what BCS had done, probably roughly in these terms: if you have this 4-fermion interaction, you factorize that interaction and then you use the factorization to solve the problem, replacing one of the products by an average; probably in those terms. I worked for six weeks and got nowhere. I got an answer, but it was the Hartree approximation rather than BCS. I came back, he told me I'd done it the wrong way, probably pushed me towards doing the factorization in another fashion, and then after that I understood BCS more or less, although of course there's an awful lot in BCS. I do not remember as well the actual reading of the paper. You are learning something about how I do physics. I'm not proud of it, but I do struggle through for myself, and find it hard to get it from the literature. It is a very standard thing in my life for people to tell me you do it thus and so, I will pick up on what I've been told, and then understand it. It's much less common for me to get it from the literature.

PoS

    So the problem that Martin gave you was when?

LPK

    This would have been a year and a half before the degree.

PoS

    And that becomes "Martin-Schwinger 2," it's really Kadanoff and Martin becomes a theoretical many-body problem.

LPK

    I haven't acquainted myself with the literature on that subject for a while, but my recollection (which is, after all, probably of interest here) is that there were Martin-Schwinger 1, 2, and 3. Martin-Schwinger 1 being the great Green's function paper that Martin and Schwinger did together. Then there was a 2 which is in fact Kadanoff and Martin, which is a Green's function theory of superconductivity based upon the BCS ideas plus the ideas of Martin-Schwinger 1. The Russians claimed, I think absolutely correctly, that they had done the same things or similar things either earlier or in parallel. I'm certainly not claiming any priority over Russians on this paper. And then there was so-called Martin-Schwinger 3, which is Kadanoff and Baym, produced in the postdoctoral period in Copenhagen largely.

PoS

    Just for getting clear in terms of background, you certainly know of everything that goes on in terms of Green's functions, and Martin and Schwinger and so forth. How much of the Russian literature are you aware of?

LPK

    Probably I was entirely innocent of it. I want to also emphasize that Kurt Gottfried was important to me in this and a little bit later period, in that he was interested in knowing what I did not understand, and capable of making me understand it. So he was an important teacher, although not in any literal sense or formal sense connected with teaching.

PoS

    Do you know Ken Wilson from those days?

LPK

    I met him once or twice. I remember sharing a car journey with him. My reaction was that he was absolutely brilliant. I thought he was just marvellously intelligent person, from the brief conversations we had. Or the brief listening that I had in that period.

PoS

LPK

    I doubt that I would have. I would have heard of it, but I doubt that I would have known anything about it until somewhat later. I do not remember whether I studied Kerson Huang's book for this period when I was learning statistical mechanics. Huang's book may have been later. I do remember that I learned something about the Onsager solution from there. I also, I think, learned it from a review paper by Montroll and others. And then I did go back to the original literature in this case and read the Onsager-Kaufmann work.

PoS

    This electron in a cavity, is that your work on the Knight shift?

LPK

    No. My thesis was published in two volumes, one which never saw the light of other publication. One of them was for the electron in a cavity, and the other was the Martin-Schwinger 2 paper, in essence, or part of the Martin-Schwinger 2 paper. The Knight shift paper was probably produced in a post-doctoral period at Harvard. There's a brief post-doctoral period after I got my PhD, but before I went to Copenhagen. This would have been in 1959. That was part of my graduate work. It was part of work which I will uncharitably characterize as reworking a whole variety of problems -- some of them classical problems in solid-state physics, some of them new problems using Green's function techniques. Just taking the new tool and applying it to everything at hand, whether you learn something new from it or not. The Knight shift paper, again, continuing to be uncharitable, is probably the only paper ever written on the Knight shift that has no component of truth in it.

PoS

    Were you familiar with Benedek?

LPK

    George Benedek, MIT? I became familiar with his work later on. I do not remember him in this context.

PoS

    Not on his work on the Knight shift?

LPK

    No, I do not remember whose experiments we were trying to explain.

PoS

    And sensitivity to experiments in general? That's part of the training?

LPK

    I don't know. I believe, as you are nicely implying, that I have characterized my work by such sensitivity. It may very well have been a part of the lunchtable conversation, it may have been something that I picked up from lunchtable conversation. Certainly the people at lunch were likely to be talking about what came out of the experiments. But I don't know where it came from.

SS

    You go to Copenhagen in the fall of 1961.

LPK

    No, this would be fall of 1960. I spent a year and a half in Copenhagen, from fall of 1960 through the winter of 1961-62. In the last eight weeks or so at Harvard, I met a person who became very important in my life, Gordon Baym. We discovered we had lots of similar interests. Gordon, as you know, is a student of Julian Schwinger. But we were working on the same kinds of things. I found him to be very intelligent and continued to work with him at Copenhagen.

    In Copenhagen, there was lots of work going on, but none (almost) in directions that were close to my solid-state, statistical mechanics interest. There was a lot of nuclear physics, with Bohr and Mottelson being the leading people in that. There was Cutkowsky, who was working on dispersion relations, and there were miscellaneous postdocs from all over the world working on miscellaneous problems. Among them were Sid Kahane from McGill working on positron annihilation. Vinay Ambegaokar (I do not remember where he got his PhD) -- he and I became collaborators after a bit. Dean McCumber, if I'm not mistaken, but we were never close, so I don't recall very well. But there was a group of Americans, and there were a group of people interested in condensed matter problems. Enough of a group so that Baym and I could lecture on the Green's function things that we had done. And we started to work on such lectures, which eventually became our book.

    At that time, I had started working on what turned into Martin-Schwinger 3, and a portion of the book, namely, how one uses conservation laws to derive correlation functions which agreed with the known conservation laws. This was triggered by the fact that Gordon Baym and I were calculating precisely the same correlation function, we got two different answers, with different factors of K and omega in them. He was satisfied with his calculation. He got the right factors for calculating, if I remember correctly, the ultrasonic attenuation. I was calculating, if I remember correctly, the conductivity, so we both got the answers we wanted, but since these were the same functions we thought we were calculating, we felt rather embarassed when we discovered this. And we then asked, how could we have gotten two different answers to the same problem, and that became a portion of our joint work.

    I had done some of the formal stuff. No, that's not the right way to describe it. I had invented, by dint of a tremendous hard work, and just plain seat-of-the-pants stuff, a whole bunch of conserving approximations. Grinding them out slowly. To tell the story of how this happened, I have to go back a little bit. It didn't have only the root in the work with Gordon on the correlation function, it had to do with a difficulty in my thesis. As you all know, the BCS theory is not gauge-invariant. That has as its consequence that if you calculate a correlation function, it does not obey what is called the Ward identity. In my thesis, I calculated that correlation function, and the Ward identity was that the left hand side of the equation should equal the right hand side of the equation. And indeed I calculated left and right, got answers of the same form, and stopped. Unfortunately, it was the same form, but there was a minor flaw. The signs were different! And so there was an inconsistency in my thesis. When this was submitted for publication, John Bardeen, who was the referee, couldn't find the error, but did the wise and kind thing and sat on the paper for eight months.

LPK

    He noted that there was a discrepancy?

LPK

    No, just sat on it (laughter). At some point, lightning struck, and I realized what the difficulty was. The solution to the problem was given by Phil Anderson in a paper which, at the time, struck me as unusually incomprehensible, in which he derives the structure of the excitations in superconductors. I believe this is the famous paper in which his version of the invention of the Higgs boson occurs. In any case, I had great troubles with that paper. I read it and struggled through the correlation function stuff. Using a formalism which had been derived by Yoshiro Nambu, whom I did not know, but apparently, I understood that portion of the literature well enough to dig it out, and ground through the construction of the appropriate correlation functions, using that Green's function formulation. I want to emphasize, since we're talking about my vision of myself to some extent, that I visualize myself, now looking back, and probably then, too, as someone of boundless enthusiasm for doing problems that were hard, and involved lots of dull algebraic manipulation. And this was that sort of problem. Hard, lots of algebraic manipulation, even when made more elegant by Nambu's technique. So little by little I was grinding through this and constructing a conserving approximation for superconductivity.

PoS

    Now we're talking Copenhagen?

LPK

    Since you caught me last time, you're not going to catch me this time (laughter). I don't know, but probably. And so there are two things that Gordon and I now have to understand. One day Gordon wanders into my office, as I tell the story to myself, and said "Well, you were telling me yesterday about conserving approximations. Here's how you construct them generally. You take this free-energy and do variational this and that and the next thing." Well, I had heard about variational this and that and the next thing from Julian just like everyone else had, but just like everyone else, I felt it was, well, "Schwingerish", but not useful for anything. Here was Gordon deriving with complete insouciance and in practically no time, stuff that took me absolutely forever to do. And I sort of said "oh, that's nice. Can you do any more of those?" He did, maybe, one more, whereupon this became one of the major threads of our book on Green's functions. And we incorporated it in our lecture series.

PoS

    You had a joint paper on it?

LPK

    Yes. It was just such a wonderful moment. I I had the problem and Gordon had the elegant method of solution and we just put them together, and it was really very nice.

PoS

    So should we think of your work at Copenhagen as a continuation of your work at Harvard, or were there new inputs into what you were doing because of being at Copenhagen?

LPK

    Martin and Schwinger had developed this wonderful technique. They went on to use it for other things. We were probably the only people in the world who were interested in using this technique to understand transport phenomena, non-equilibrium stuff at long wavelength. What we had to do was to find ourselves a bubble, and hide in that bubble. Sort of semi-isolated, but stimulated by people who cared about physics. And we found that in the post-doctoral period. That's not entirely true. For example, Ambegaokar and I wrote a paper on just exactly the subject in that period, but mostly the two of us lived our lives in this problem. Again, Gordon did other things then, but as I see it, we lived our lives in this problem in the environment of good physics, international people, people from all over the world, and leisure to think that was provided by Copenhagen.

PoS

    Would it be fair to say that at this point you conceive of a description of the microscopic world in terms of Green's functions, rather than, say, the field theory behind it? I'm interested in the mode of description, the language employed in trying to understand a work.

LPK

    What you say probably would be true, were this the high point of my career. These were the best toys of my youth, but this was not my mature scientific career. I have a world in which I live, but it is a world of critical phenomena. It's a world of self-consistent behavior, and not a world, I don't think, of Green's functions. I may be mistaken, but I think Green's functions are a toy that I've put away or a tool that I have in my closet to take out from time to time, but they're not a crucial part of my world view. On the other hand, just to follow you where you're taking me, I would say that my view of the world is conditioned on correlations. And if you push me a little further, that's correlation functions, and if you push me a little further, that's Green's functions. But worrying about how the frequency comes in, and doing frequency sums, I haven't done that in recent years. That was then, this is now.

PoS

    No, I meant more in terms of what constitutes your toolkit in addressing the problems as you face the world. That's all, really.

LPK

    Well, amusingly enough, the major portion of my toolkit was brought to me by Gordon. It's the free energy, the thing I didn't think I had absorbed from Schwinger. It's the idea that you have a generating function. Now that was part of my thesis with Glauber, too, generating functions were there, and for all I know it may have been part of my work with Martin. I think the free energy, the generating function, has provided a very major portion of my toolkit.

PoS

    What's in the back of my mind in asking is how do you formulate it, and how do you get to the problem of Kadanoff and Martin hydrodynamics Green's function and that connection -- going from the macroscopic to the microscopic rather than the other way around?

LPK

    There were two discrepancies, and we see now that they come out two different ways. The two discrepancies that I mentioned to you were the gauge invariance in BCS, and the behavior of the correlation function in transport phenomena, as Baym and I saw it. Now, this requires two things. I said I only had a few conversations with Schwinger. Schwinger was the great mind of Harvard at that day. The Nobelist, an amazingly intelligent man who was a little inaccessible. Despite the fact that I ate lunch with him every day for years and years and years, three times a week, for years -- a little inaccessible. But we brought these discrepancies to Julian; I remember just sitting in a classroom with him and Martin explaining the discrepancies. And he produced words roughly to the effect that what you need is a physical understanding of what's going on, plus a method of calculating that includes that physical understanding. I'm not remembering very well, but despite the fact that I don't remember, it was an important event in my life.

    Now part of it was then the development of the formalism via the Green's functions. Part was something that Martin and I picked up on after the Copenhagen period, I think, in which we looked at physical behavior, and asked what was the implication for the behavior of correlation functions. And we did some, in my view, excellent work on this subject, important paper in my opinion, not made less important by the fact that Landau and Placzek had done work with similar content. And published in some, I believe, rather obscure place. I do not know whether I ever saw the Landau-Placzek paper, but it is said to have similar content, and that is easy to believe. In any case, Martin and I put together this paper, I think in the period just after Copenhagen, but I'm not remembering very well. And it, then, was the other great achievement of this series of things which begins at Harvard and ends in Green's functions and correlation functions. And then there is a major breaking point in my scientific life as I see it. (break)

Continue reading part II of the interview.