A Career in Theoretical Physics

The following sections are included:

• PREFACE TO THE SECOND EDITION

• INTRODUCTORY ESSAY TO THE FIRST EDITION

• CONTENTS

• More Is Different

This is a condensation of most of my thesis. For two years of postwar grad school, 1945–47, I took the (mostly wonderful) courses available at Harvard from Schwinger, van Vleck, Furry, and visitors such as Goudsmit and Gorter, and, aside from that, enjoyed myself, eventually winding up as one of a group which congealed around Tom Lehrer, Dave Robinson, and others like Chan Davis and Bob Welker, which was more about bridge, singing, puzzles and scifi than physics. I had the GI Bill and a tiny scholarship, and would have been happy to go on indefinitely as Tom Lehrer actually did. But in the summer of 1947 I met the right girl and things suddenly became more serious. Van had given me, as one of his last three graduate students (another was Tom Kuhn), a marvelous problem, in spite of my marginal performance on my qualifying exam. It arose from one of the postwar revolutions in spectroscopy which radarderived coherent sources allowed, unprecedentedly detailed molecular spectroscopy. I solved it using a series of novel techniques borrowed from Schwinger's courses among other sources. I felt that after this there was little more to be done in this field and wanted to move on to other things, an attitude which one job interviewer interpreted as reprehensible, and chose not to hire me…

This is my first review paper — a forerunner of the “soft mode” paper of 1958. Bill Shockley hired me at Bell to work on his ideas on ferroelectricity and I did, but soon became more interested in generalities, feeling that calculations were premature. He was unhappy with my work, which seemed to ignore his ideas for detailed calculations; but he taught me a lot of solid state physics and the background and the experience were both valuable to me…

These lectures, given at the very young Yukawa Institute as a final thanks to Japan, for my Fulbright visit in 1953–54, are a summary of my approach to line-broadening problems, the field of my thesis and of much of my early work at Bell. During my stay with Kubo in Tokyo he began to go on with these ideas to develop the correlation function methods which became so important in condensed matter theory. (As did Lax at Bell, but not with so much effect.) My paper with Weiss in Rev. Mod. Phys., in spite of its appearance in a review journal, was not a review. Several reviews appeared on my approach to pressure broadening but none were by me…

Gregory Wannier and I, as well as B.T. Matthias and Jack Gait, showed up for work on the same day at Bell Labs. At least two of the four of us (probably the theorists) were surplus to “nosecount” and so it was not surprising that they put Gregory and me in a big office together. Chatting with Gregory was a great learning experience for me. A year or so later Charlie Kittel came wandering into our office and asked, “Do you know about antiferromagnetism? Why don't you work on that?” He must have just heard about Shull's neutron diffraction experiments demonstrating its existence, and of course its relative, ferrimagnetism, where the spins do not compensate, was of great interest technically, and was soon to be the subject of beautiful experiments at Bell by William Shockley, and later Gait, on domain wall motion. Our negative answer to Charlie's question was soon corrected, Gregory producing a well-known paper showing the non-ordering of the triangular Ising lattice, and I produced several papers of which the first two earned me an invited paper, independence from Bill Shockley, and a raise, though they were not sparkling intellectually. Although Kittel's stay at Bell was brief — he was soon to decamp for Berkeley to space opened up by their “Loyalty Oath” losses — he was very influential at that early stage in my career, and in moving research at the Labs into new directions, for which Shockley did not thank him…

This is the aforesaid soft mode paper. I went to Moscow to meet the Landau group and to talk with them and with Shirkov about superconductivity, but the invitation was to a dielectrics meeting. The work was from my notebooks of 1950–54, and I felt that in sending me Bell was paying me its “dielectric bill” for all that work under Shockley…

This is the best-known of a number of papers I have written involving what are now known as “frustrated” lattices, lattices into which it is hard to fit an ordered state. The first was one of my earlier papers on antiferromagnetism referred to in the discussion of the previous paper, and of course Gregory's triangular lattice paper had the same theme; I also had a summer student, Frank Stern, do spin wave calculations on a facecentered cubic antiferromagnet to show that it wouldn't order at finite T, which he published in 1954 under his own name. The subject is fashionable these days, so this is getting a late burst of citations, probably undeserved…

There followed in 1957–9 a small-scale version of an Annus Mirabilis — no invidious comparison with Einstein intended, just that this kind of sudden creative flowering does happen with some generality. One possible causative factor was a change in the situation at Bell Labs — after a series of losses of major theorists including Bardeen, Kittel, and shortly H.W. Lewis and Wannier, Bill Baker, then the vice president for research, decided to encourage us to form a separate theory department rather than being beholden to experimental masters. We (Peter Wolff, Conyers Herring, and I) responded by escalating ourselves into a full-scale academic department with postdocs, an elective chairman, and many other privileges such as relatively casual travel and sabbaticals, which were standard in academic physics at the time but unprecedented in an industrial lab. Also for a couple of years we had an extensive summer visitor program including nuclear and particle physicists such as Keith Brueckner, John Taylor, and John Ward as well as an expansion of our solid state visitor program — to Walter Kohn and Quin Luttinger we added among others Philippe Nozieres, David Pines, Elihu Abrahams, and as a summer student Bob Schreiffer. To this was added substantial salary improvement, since our losses at that expansive time were often to better-paid academic jobs. In the year 1958 I produced this paper, on which my Nobel prize was mostly based, as well as the papers on gauge invariance in superconductivity, the paper on superexchange, and the dirty superconductor paper. (The soft mode paper was older work.) The gestation of this one had occurred in 1956 while I was still in my house theorist mode, but it gained from the independence and self-confidence of the new PWA…

This Letter, sandwiched in between two much longer papers on the same subject (Phys. Rev. 110, 827 and Phys. Rev. 112, 1900), summarizes very succinctly their conclusions and method. It not only solves the dilemma of gauge invariance but presents my somewhat primitive version of the new methods being invented in manybody theory by Martin and students, by Montroll and Ward, and above all by the Russian group around Gor'kov — I called mine the “equation of motion” method, and it was almost simultaneously presented by Morrel Cohen. My “Babylonian” emphasis on the problem at hand probably saved me from further involvement in what was in fact a very fruitful but very crowded area of research, competing with all these brilliant people, and sent me off into other directions…

In that eventful year of 1958 I had time to spend two months visiting Charlie Kittel's group in Berkeley. I replaced Freeman Dyson, his summer visitor for the previous two years, and benefited from the considerable funding Charlie had found for Dyson only to the extent of our having a marvelous house perched on the Berkeley hills next to the Radlab. Many people — Cissie Geballe, who was out visiting her influential family, Jim Phillips, Charlie himself in spite of an earlier squabble not worth mentioning here, and Tom Lehrer being at the Hungry I, among others, conspired to make our visit a pleasant and interesting one, and a chance encounter with Leslie Orgel provided the final key piece of this paper (as I remark rather redundantly in the notes on the next paper.)…

This introduces the importance of time reversal to superconductivity and the scattered state representation which was used so ably by Tsuneto and by the de Gennes group.* The names “Dirty Superconductors” and “Dirty Limit” are used extensively to this day. The ideas were developed during a summer of enjoying Charlie Kittel's hospitality at Berkeley in 1958, and actually written up before (9), which was in winter '58; but the publication was delayed by problems at Pergamon Press. To me this paper and its implications were the conclusive experimental proof of the essential correctness of BCS, because superconductivity's insensitivity to most impurities is such a striking, universal fact, while its extreme sensitivity to magnetic impurities is equally striking. Many people seem not to understand the great logical force of such an argument…

This paper mentions that there will be structure in the energy gap function associated with phonons: when I brought this out in a talk at Birmingham in late '61, R. Peierls asked how it might be measured. At most a few weeks later I heard from J.M. Rowell at Bell Labs, that it had been, in the tunneling characteristic. The next few years left BCS with a sound quantitative basis. The paper owed much to Schrieffer's discussions with me and with Pierre Morel, my student inherited from D. Pines; Pierre was simultaneously serving as science attache at the French embassy…

Pierre was my first serious student, and as is often the case he was among the best. He was bequeathed to me by David Pines, who had left Princeton for Illinois, and couldn't move Pierre from his job in NY. This paper later got Pierre his first promotion in France, when there was a brief but unconfirmed flutter about discovery of the He-3 phase, but of course we were 12 years previous and wrong about L. Nonetheless Pierre went on to a distinguished career in space science…

This paper was mentioned in my Nobel Prize citation along with localization and superexchange, causing a slight frisson of guilt in me because I learned about resonant states from a talk by Blandin at a small workshop on magnetic metals at Brasenose College, Oxford in Oct 1959. (We were not slow to take advantage of our new freedom at Bell to travel; this was my third European trip in ten months.) Friedel and Blandin's ideas had only the weaknesses that they were not focussed on the specific problem I addressed, which as noted in the paper arose from Matthias' question; and that they used a generalized notion of “exchange”, not emphasizing the Mott-Hubbard “U”. In a meeting abstract Clogston and I pointed out that therefore some details might be different — signs of couplings, for instance, about which I won a bet against Walter Marshall made at that same workshop. Friedel's work on alloys and impurity states deserves more recognition than it has had. Nonetheless the “Anderson Model” has had a long and not wholly undeserved run…

The physics behind the Higgs phenomenon is not, in spite of the belatedly added reference to Schwinger's opaque remarks, in any way beholden to Schwinger in its inception, since it was a direct transcription into particle language of my work (referred to above) on broken gauge invariance in superconductivity. My ideas on broken symmetry in both vacua and in condensed matter systems did receive great impetus from some brief contacts with Y. Nambu: his phrase “independent orthogonal Hilbert spaces” was very liberating and expressed what I had been groping towards since 1953. I also brushed shoulders, at least, with Steve Weinberg at the Cavendish; and as I acknowledge, J.C. Taylor was at Bell for a summer and we talked at length. Higgs acknowledges this paper as the source of his ideas. Brout was a friend and a regular visitor at Bell, but I do not remember if we discussed this subject…

The point here was a demonstration theory that flux lines do move and cause dissipation, which was a totally new and deep concept; not the specific assumptions of the model, which have been occasionally set up as a straw man in subsequent work. Kim noticed the slow decay of magnetization in the “critical state” and I proposed a logarithmic fit, on the basis of a “creep” mechanism like that of dislocations. Later we observed flux “flow”, as well as noisy “flux jumps”. But the exciting idea was the generalization of old ideas of dissipation by dislocation motion in solids to the general concept of defect motion in ordered systems: the genesis of one of the main lines of the theory of broken symmetry. We thought this work very important, and were unhappy about Bell management's decision to oppose publicity for it, on the basis of Matthias' and Geballe's objections that it negated their discovery of high-field superconductors…

Having discussed his theory with Josephson and others at the Cavendish, where I spent the academic year 1961–2 at the invitation of Neville Mott, and as an early Visiting Fellow of Churchill College, I alerted John Rowell on my return to the probability that the effect predicted by Josephson was real. I am on the paper because I helped devise ways of making sure it was not a short in the junction; and because under the necessity caused by actually seeing the effect I had to understand why others hadn't and thus to begin to understand the whole concept of coherence and generalized rigidity. I now believe that Giaever may have seen but ignored it. A few months later Ali Dayem and I demonstrated the AC Josephson effect in a metallic microjunction, giving Bell Labs a strong patent position in Josephson devices which they ignored. (For quite a while all SQUIDs were point contact and would have been covered by the patent. They may still be for all I know.) I have been accused of “exploiting” Josephson's discovery with these patents, but after all that's what Bell experimentalists are paid for, and the two experimentalists were the real “discoverers” — we had no intention, or possibility in law, of patenting other than our own discoveries. I went to great lengths, and succeeded all too well, to avoid the Matthew effect with Josephson, thereby depriving John Rowell of much of the credit he deserved…

John was reluctant to exploit the Josephson Effect too extensively because we thought this line of work more important — it was after all the ultimate experimental proof of the BCS mechanism. We took the data down to Penn to show them to Bob Schrieffer, who I knew was developing an on line gap-equation-solving capability. Thus I returned the favor he had done Morel and me by pointing us toward Eliashberg. He and students Scalapino and Wilkins provided an accompanying letter using our suggested modeling of the phonon spectrum. I wrote up all this history in 1987 as “When the Fat Lady Sang.”…

In the Buhl lecture of 1963, I talked about the “magnetic state” which characterizes all strongly repulsive systems, an insight still very valuable and unavailable to those trained in the school which nearly monopolizes U.S. solid-state education, and which emphasizes band calculations and one-electron theory. This latter school is very much beholden to the influence of J.C. Slater and his students. The motivation for the Buhl lecture was really Bob Shulman's simultaneous infatuation with his Jaguar and with food and wine; the former took us to Pittsburgh to partake of the latter unforgettably, with Bob Heikes and his wife. Heikes ran the workshop and, before his distinguished management career, contributed interesting ideas in this area…

A relic of my (mostly) love (some) hate relationship with Bernd. I came to be sure, even before 1987, that the full story of many superconductors included something new, while he became increasingly depressed by the evidence that phonons were right. Bernd's great strength was his refusal to play by other people's rules. With the metallurgists and chemists who were his natural competitors he exploited the narrowness of vision which led them to synthesize and characterize compounds in traditional ways, without recognizing that modern solid-state physics had opened up a cornucopia of useful and interesting classifications such as ferroelectricity, ferromagnetism (“pro” or “anti”) and superconductivity, which could be recognized with essentially trivial measurement techniques. With theorists, it was our focus on simple models and simplest cases which was the Achilles' heel he found and, to be sure, used to the hilt to mystify and confuse us. The theorists loved to make elaborate theories of complicated effects, requiring beautiful precision measurements on the simplest, cleanest possible materials. Their success in doing this convinced them that they had “solved superconductivity”. But Bernd realized that the average nonspecialist had no idea of the intellectual structure of the field and that, to him, the proper role of theory is to predict whether substance A or substance B is superconducting at all, and if so what is its critical temperature. (Reporters are the ultimate nonspecialists, but even physicists in other fields fall easily into this mode of thinking, and in fact one completely ignores it to one's peril.) Such questions are extraordinarily difficult, in large part because the answer comes mostly from negative results: substance A contains atoms Z, X, and Y which can combine in thousands of different ways, all of which must be less stable than A for it to exist at all in the given chemical state; it must then choose the physical state (crystal structure, magnetic structure, electronic structure) which favors superconductivity. So one is asking the theorist to do thousands of (to him) irrelevant calculations, most of them impossibly difficult, before he starts. To make the situation clearer, perhaps as many as a couple of dozen crystal structures, and no melting points, have been calculated accurately from first principles; and T_c is in principle (though not in fact) very much more complicated than either…

A first shot at a general theory of broken symmetry and at the implications of the Josephson effect; as such much shorter than my article in Gorter's Progress in Low Temp. Physics of 1967. The discussion remarks are important: they refer back to a paper (not in my bibliography) taking issue with a remark of Gorkov and Galitskii, and reflect my growing conviction that broken symmetry has a lot to say about the fundamentals of quantum mechanics and vice versa…

I feel this is the cleanest discussion of superfluidity available. Note that on many points this is contradictory or orthogonal to Landau orthodoxy as pronounced by Khalatnikov. Whether Landau would have agreed was never clarified because of his accident…

At the Varenna School, 1966, there was a delightful gathering of the magnetism world organized by (eventually, Lord) Walter Marshall, in the heyday of the Varenna School when it was still possible to swim in Lake Como safely. Many contributions were good — I remember those of Volker Heine and Jim Phillips especially. There is much useful formalism in the discussion of Friedel's theorem and the Anderson model, but the actual calculation for “liquid Fe” is flawed by a serious program error discovered by J.M. Olson, a student of Kohn. Bill and I carefully never assigned the blame for this…

This was stimulated, as I acknowledge in the paper, by discussions with John Hopfield about his student Gerry Mahan's calculations, which didn't seem to converge, on the x-ray threshold, and by the widespread skepticism about that work engendered by Kohn and Majumdar's very convincing demonstration that seemed to say that the Fermi surface did NOT cause any singularities. This led on into the whole corpus of work on the Kondo effect. It is also noteworthy in what I missed. First was that the determinant is a Cauchy one and may be directly evaluated, giving the dependence on the phase shift itself, not its sine, which also shows that it is a non-perturbative result. (This I learned from Quin Luttinger and put in a later paper.) But more important, I did not realize that with the only dynamics being a constant Fermi velocity, the singularity in volume may be immediately converted into one in time, giving the power-law spectrum for X-ray edge singularities soon to be derived by Nozieres and de Dominicis. This was Gideon Yuval's observation. Later in '67 I began my transatlantic commute to the Cavendish, where I was nominally the Professor and group leader for solid state (soon renamed condensed matter) theory, and Gideon was one of my first few students…

The following sections are included:

• The Kondo Effect. I

• The Kondo Effect. II

• Kondo Effect III: The Wilderness—Mainly Theoretical

• Kondo Effect IV: Out of the Wilderness

This is an elaboration on and postscript to paper 19…

Trieste, 1968; Salam's last convening of the whole of theoretical physics. This meeting followed on from Kyoto 1953 and Seattle 1956, both of which I attended but gave no major talk. (At Seattle I spoke briefly about my first blundering steps towards localization.) The meeting came in June '68; I remember hearing the news of Robert Kennedy's assassination as I drove across Northern Italy from a NATO meeting in the French Alps which was dominated by discussions of politics. But at Trieste the only fuss was made by various of the Nobelists, who objected to being sequestered in Duino Castle. There was an excellent pre-meeting program on molecular biology by Crick, Brenner and Klug which to me was the most exciting part. I was dissuaded from talking on the Infrared Catastrophe; by request, instead, I repeated much of papers 20 and 21…

I left localization in 1958–9 for superconductivity, not because I had any doubts about the result, since the paper was practically a proof and Feher's ENDOR method couldn't work without it, but because I was bemused by the strong interactions between real electrons. Mott deserves all the credit for nursing my dream into the real world, and here is the first evidence that even I had become a believer. I saw at last that Mott and Anderson insulators were complementary and indispensible to each other. That is, repulsive interactions will necessarily make even fewer final states available for coherent hopping processes at the Fermi level than are available for non-interacting electrons. Elihu Abrahams and Nevill Mott had, between them, built a whole transport theory on my ideas, which Mott proceeded to correlate with experiments. This paper marks the prodigal's return to the subject…

ILTP Kyoto, 1970. My “Infrared Catastrophe” paper which, after Mahan's work, instituted the subject of Fermi surface singularities, led on through Nozièresde Domenicis' ideas to the long-range interaction between spin flips in the time domain which is the secret of the Kondo effect. Then to solve the resulting statistical problem we had to invent a version of the renormalization group. It is not the same as Wilson's but it is very useful and it was earlier. And we did solve the Kondo problem, although Ken Wilson has never given us credit for our priority. This is a very brief review of these developments, which were very much furthered by Gideon Yuval, with John Hopfield as a hidden collaborator and Don Hamann contributing an important generalization…

This paper was almost complete by the time Chandra and I had returned to our offices after hearing for the first time Bobby Pohl's talk about his remarkable experimental results. It seemed to write itself, requiring only Bert Halperin's characteristic cleaning up of our slightly sloppy logic. To me it seemed then and seems now that it is merely a restatement of the experimental facts; yet to this day, after three decades of theoretical effort, there is no consensus for a less heuristic description of those facts. But it does have consequences, profound ones, for the nonlinear responses, and it remains one of the most cited papers for each of the three of us…

The following sections are included:

• COMMENTS ON THE MAXIMUM SUPERCONDUCTING TRANSITION TEMPERATURE

• Comment on “Model for an Exciton Mechanism of Superconductivity”

I was one of many people invited to contribute to a Pauling Festschrift in this journal, which accounts for the surprising placement of this paper. But Rustum Roy, the editor, thought it was simply an over the transom submission, so I missed the festschrift. Although I admire Pauling's great intuition as a chemical systematizer, I had been assigned his paper on metals to review in my early days at Bell, and had seen it as a fudging job which missed many of the essentials, trying to do band theory without band theory — so there is a slight tinge of irony in the title. This was a stab at taking Pauling's RVB and making something physical out of it. I finally began to get an inkling as to how to properly describe an RVB state in '87; the present paper was only a hint, further developed in later papers by my visitor Patrik Fazekas…

I cannot leave out of this volume entirely the wonderful years spent working with Bill Brinkman, Doug Osheroff and my student Mike Cross (and others: Joe Serene, Chandra Varma) on Helium-3. Summer of 1972 was when John Wilkins sat on the lawn at the awful Beaver Dam Gordon Conference site and told us all about the magnetic resonance results of Doug Osheroff and friends, and I realized soon after that that the two liquids were those described by Morel and myself, and Balian-Werthamer, but how to prove it? A crude attempt by Varma and me was trumped by Leggett's wonderful theory, and one by Bill and myself was both second and inferior. But in this paper we at least explained the microscopic why of it. The big review Bill and I wrote was rejected by Rev. Mod. Phys. but is available elsewhere. 1973 seems to have been another great and busy year, entirely aside from the delicious Nixon hearings…

A summary of the Nobel symposium at Aspenasgarden near Goteborg, June 1973. A light treatment with some still useful thoughts about the renormalization group. Like many such summaries, it was composed hastily to say the least; however, unlike many, it had a great deal to report on: the Kondo effect, the phase transition work of Kadanoff, Wilson, Fisher, the first serious progress on superfluid He3, and the x-ray edge work were all very recent. It was the second great period of condensed matter physics…

Another version of paper 28: more complete, perhaps less careful. Yuval wrote it and he is a bit slapdash…

This is a summary of the physics in Inkson's thesis which explains fairly clearly why local self-energies (the LDA) don't get energy gaps right. Inkson and I felt that these considerations were widely ignored, and then rediscovered, without much acknowledgement, by those more in the mainstream. The methods resemble those of the Swedish school. Inkson was for various reasons unable to publicize our work very much, while this rather obscure place is the only time I found to talk about it, so we are at least partially culpable if there is any blame to be assigned for its neglect…

This paper was one of a cluster by the three of us, a cluster mainly because we gave them separately at different meetings. The real work was by the two of them — I think I had just a few long discussions, especially with Patrick, and am a little shamefaced that my name got on all of them. They have been very much cited, so seem to have been needed, although now they seem rather obvious…

This is a retrospective view of my slant on the origins of broken symmetry in particle and condensed matter theory; staking my claim to have first seen the necessity for the Goldstone boson as well as the Higgs…

Somewhat speculative but I still believe that the negative U center plays a very big and interesting role in the electrical properties of amorphous semiconductors, photosynthetic centers, etc. I remember walking a hair-raising trail 1500 meters above Grenoble with a big group including Friedel, which had consumed great quantities of wine with lunch, as part of the Au Trans meeting at which this was given. The late Michael Schluter, as well as Gene Baraff and Don Hamann, actually showed later that such centers are possible by explicit calculation of the Si vacancy center. But the mobile bipolaron which many people have proposed for superconducting phases is undoubtedly a figment…

Sam Edwards had been chosen to fill the professorship left vacant by Otto Frisch's retirement, but was not available yet because he had another year to go as head of the SRC (England's NSF, roughly). I was about to end my years of transatlantic commuting, reluctantly — Joyce and I felt we had to be on one side or the other, and it didn't matter much which — so Sam and I were kind of ships which passed in the night — or actually, met over coffee on Saturdays in the Cavendish CMT group for half of a year. He was at loose ends for a problem, and I described to him the evidence that there was a spin glass phase transition, and that I thought the key was frustrated randomness — as we now would call it. We share credit, I think, for the idea of order in time, not space — non-ergodicity — but he pulled the replica method out of an old notebook, and there we were. We had no idea the consequences would be so wide-ranging…

My former student Richard Palmer had been brought to Princeton by John Hopfield, so he was waiting there when I arrived in Fall 1975, (also with John's help) but Palmer left after a couple of good years. I don't remember quite how it happened that David Thouless was there, but David Sherrington came down from IBM and I put him up for a while in my Princeton housing while we all discussed the problem of negative entropy in the Sherrington-Kirkpatrick replica solution, which was Edwards-A for the case where mean field should be correct. What we constructed is equivalent to the old “cavity method” of Onsager and Bethe-Peierls, although we only later noticed that. From spin glass it has morphed into computer science in all kinds of guises as a named algorithm — “preference theory” is one; this development was via the wonderful work of Virasoro, who showed it in principle as good as Thouless-Parisi replica-symmetry-breaking. Richard and Scott K. independently discovered the inconvenient fact that solution of any given case is NP complete, which led to the idea of a stat mech approach to computer science, which Scott pioneered by producing the simulated annealing algorithm, which is just the description of how he and Richard proceeded in finding solutions, as described in this paper…

My only substantive contribution to the topology revolution wrought by Toulouse-Kleman and Volovik-Mineev was this, where we inter alia pointed out the further problems with precisely defining superfluidity that the existence of topological textures could cause. Everyone, myself included, thinks topology is a fancy way of describing the obvious until he's confronted with the 4π texture, as I was by Gerard. Dan Stein and I also discovered the “boojum” independently of Mermin but didn't think of as good a name for it — for which feat I think David deserved the credit he got…

The “Gang of IV” paper. I had the idea of fitting the classical and localized limits together with some kind of interpolated scaling curve in the midst of a lecture one day. Then it was at lunch the same day with Elihu, who often dropped in at Princeton, where I maintained a visitor office for him, and Rama, who was with us for several years off and on, that Rama recalled the old diagram work by Langer which we used as a starting point. He and Elihu then rapidly put together the resummation of backscattering diagrams which is “weak localization theory”. Don L did some simulational verification for us; besides, the original inspiration for a scaling theory borrowed a lot from Licciardello and Thouless' earlier paper…

This is my most complete summary of the theory of broken symmetry in condensed matter systems…

The “Glitch” phenomenon is nearly an unequivocal proof that neutron stars are at least partially solid. It is very hard to obtain two time scales differing by ∼ 10¹³, with no intermediate scales, without a breakdown of rigidity. Ruderman, Pines and Shaham proposed actual “starquakes” caused by the strains generated by spindowns, but soon accepted the mechanism Itoh and I proposed in a brief letter in Nature, of “vorticity jumps”, equivalent to “flux jumps” in a superconducting magnet. Our letter was given an award by the Observer magazine for “the most incomprehensible title of the year”. Pines and Shaham are responsible for introducing me to the Aspen Center for Physics, which played a great role in my life on my return to the US in 1975 and for 15 years thereafter. We wrote too many papers on too few data, of which this is a typical one, but this is perhaps natural in view of the generally apathetic response to our work in the astrophysics community…

This is a final summary of my work in the second “weak localization” period of localization theory, which was inaugurated by the “Gang of 4” papers in 1978. During this period we all (Abrahams, Fukuyama, Vollhardt and Wölfle, Ramakrishnan, Lee, Thouless and occasionally some Russians) met regularly at Aspen in the summers. This cooperative stress-free atmosphere seems to have been a casualty of high-T_c, funding and job shortages, the cutbacks at Bell and IBM, or a combination of these: it doesn't exist any more…

This is part of the cooperative development discussed above, but has always had a special place in my mind as most foreshadowing what were to be the next series of developments: the “universal fluctuations”, quantized resistance, etc, most of which are corollaries of this point of view. This was the third way of looking at localization, one channel at a time — pioneered decades before by Rolf Landauer, but in a way also contained in my original paper, which emphasized the singular distribution of path amplitudes. It makes the GIV technique's dependence on averages over randomness look shaky indeed…

This is the first or at least one of the first papers about what is now called “nanoelectronics”, which excuses its appearance here. Engquist came from Sweden on his own money, and it was a pleasure to work with him; but his health has several times prevented his return…

This is one of a sequence, of which more complete versions were produced with the help of the computer skills of first Dan Stein and next Dan Rokshar, then an undergraduate. I include it to selfishly stake a claim as one of the co-inventors of the “rugged landscape” evolution model, along with Gerard Weisbuch, Stu Kauffman, and no doubt others. This was the gestation period of the science of complexity, and I met all kinds of wonderful people doing similarly speculative things in wonderful, if sometimes weird, places — Keystone, CO, Dubrovnik, Werner Erhard's mansion in San Francisco, Klosters, and, eventually, we congealed around the Santa Fe Institute…

This is my best review of the “chemical pseudopotential” theory, a methodology which is meant to clarify many of the empirical facts of chemistry, such as locality of bonding, the meaning of ions in molecules and solids, the meaning of directed bonds and bond-angle forces, etc. It seems to be wholly out of synch with modern trends in theoretical chemistry; chemists do not ask the “why?” questions but only calculate particular cases…

My contribution to SFI's founding Workshop. The evolutionary biology line has been much exploited by Kaufmann, Weisbuch, Fontana and others associated with SFI…

This is the most precise (and concise) statement I can make of my attitude towards the fundamentals of quantum theory. It says nothing which does not seem self-evident to me, yet Leggett disagreed strongly, although he now seems to have changed his mind. I had no idea that the experiment of causing two separately cooled Bose liquids to interfere, mentioned at the end of the paper, would be carried out so soon, as it recently was on two Bose gases. I believe this paper was the first to suggest it, and the outcome was exactly as predicted here…

This was mostly paraphrased by Lilian Hoddeson in her book on the history of solid-state physics; this is the original, unpublished version…

The following sections are included:

• SPIN GLASS I: A SCALING LAW RESCUED

• SPIN GLASS II: IS THERE A PHASE TRANSITION?

• SPIN GLASS III: THEORY RAISES ITS HEAD

• SPIN GLASS IV: GLIMMERINGS OF TROUBLE

• SPIN GLASS V: REAL POWER BROUGHT TO BEAR

• SPIN GLASS VI: SPIN GLASS AS CORNUCOPIA

• SPIN GLASS VII: SPIN GLASS AS PARADIGM

These are three of the several reviews I gave of the mixed valence problem in the years from '75–'87. My students made appreciable progress, especially Haldane and Coleman, but I felt and feel the problem has never been sorted out. The first review states the problem; the second gives some vital advice to prospective solvers; and the third represents my final state of confusion…

When I began to prepare these lectures, and to wonder what I could possibly say that hadn't already been said by all the brilliant lecturers you have already had, I began to realize how many years I have actually been associated with the problem of “Moment Formation”. As I have often explained, I don't actually quite go back all the way to the first exploration of this problem, since the virtual state concept was originated in fact by Blandin and Friedel in early 1959¹ or so, and I heard a discussion of it by Biandin in 1959 at Oxford, which stimulated me to develop the model of which so much is made in the mixed valence field…

The following sections are included:

• Introduction

• Simple ideas

• Chemistry of mixed valence

• References

This now seems much more relevant than ten years ago — the methods Dieter and Peter developed are having a rebirth in the cuprate problem. And it really does solve the problem for spin fluctuation theory that Philippe Nozieres pointed out years ago, that the susceptibility doesn't diverge; formally Fo_A approaches −3/4, not −1, i.e. it goes to a constant Wilson ratio. The real work of calculation was all Dieter and Peter's. It began, as I remember, at Aspen…

These two lectures were given in Japan in 1989 at the behest of Ryogo Kubo. Kubo Sensei was an early soul-mate: he claimed at one time that he “discovered” me, which was certainly in a sense true, in that he arranged for me to be at the Kyoto 1953 meeting where I made many vital contacts; while I certainly have enormous respect for him both as scientist and as organizer…

I may not be a very appropriate representative for the subject of Materials Science here in a conference focusing on technology and the applications of science to human problems. I am not, strictly speaking, a materials scientist in the narrow sense of these words, and much as I admire and applaud the applications of science in technology, that is not what I do. I am a theoretical physicist much of whose work has involved trying to understand the behavior of more or less complex materials such as metals, magnets, superconductors, superfluids, and the like. I thought that perhaps you would enjoy hearing, in the brief time I have here, not about these investigations or about wonderful materials of the future—as far as I am concerned, from an intellectual point of view, the very impractical and obscure low-temperature phases of the mass-3 isotope of helium are at least as fascinating materials as anything the future is likely to bring—but rather about some of the wider implications of the kind of thing I do…

This was my first full-fledged discussion of the high-T_c phenomenon. The amazing thing to me is not how much is wrong with it but how much is right. At this time the whole RVB idea seemed so straightforward that the gaps in the arguments should fill themselves in the natural course of things. This was not to be the case: several questions which I posed in my final summing up turned up to contain vital parts of the story.

Nonetheless the basic idea of a projective ground state was correct…

This paper was rather rudely rejected by Nature, and since it has been fairly widely circulated (and cited) I didn't further push for publication. Nowadays it would be on the web and snoot to the referees. It was later shown to be correct in essence by Gunnarson via detailed calculations, and my impression is that the problem it poses is only recently being solved by the group of Capone et al…

I enjoyed doing these “Reference Frames”, of which this is fairly typical, under the aegis of Gloria Lubkin. It expresses my discomfort at the gullibility of scientists in the face of anomalous but marginal results…

The Institute's steering committee, acting as a committee of the whole, organized, in summer '93, a meeting searching for common threads — integrative themes, we called them — of our approaches to complexity, for which this was meant as a prologue. I don't think the SFI ever rose again to this level of collective discussion, to my knowledge, so, incomplete as it is, I include my contribution. I did a couple of lecture series on complexity but never wrote them down, so this will have to do…

David and Steve were my last two students, also wonderfully good, and came along to Oxford with me as postdocs. I couldn't leave out this, as one among several substantive things we did, especially since the “magic angles” we talk about have reemerged as interesting. The two of them were casualties of my stubbornness about interlayer tunneling + the sociology and politics of the job market, but at least are much richer working in the financial world than they would have been in physics…

I organized (with more help from Ken Fulton of the NAS than I should have needed) a “colloquium” for the NAS on complex aspects of physics, shortly after I got home from the Eastman Professorship at Oxford in '93–'94. The papers were great, the attendance miserable, the facilities at the NAS West very nice…

I gave this lecture in Frankfurt in a series sponsored by the Deutsche Bank. I don't know whether they published anything; I gave them only my bare transparencies, but then I wrote this out and may have sent it to them. To my knowledge it may be the first hint at the now fairly popular explanation of Pareto wealth distribution laws…

This was a review of a book called “The Dappled World” by the philosopher Nancy Cartwright. I have done a lot of reviewing in these, my declining years, and have spared you most of it, although I think the reviews contain a bit of originality scattered here and there. In this paper I was encouraged to make a bit of an essay of it and since it summarizes some of my ideas on the epistemology of science I include it…

In 1995 I finally accepted first the d-wave nature of high T_c cuprates, and then by '96–7 the experimental proofs by Kam Moler and collaborators, and then by Dirk van der Marel's group, that interlayer theory wouldn't work. Where I went wrong was in believing too firmly in my “dirty superconductor” “theorem” and rejecting d-wave in the first place; and because of not realizing that some form of spin-charge separation could fix that. I had to rethink and return to basics. The period '96–'99 was occupied with a number of papers on the way to this rethinking, and I've omitted these as perhaps only part of my autobiography, as Landau used to say. There are a lot of interesting ideas there, but it is too hard to separate the gold from the dross. I also wrote a number of polemics dedicated to the underlying idea that the cause of high T_c was still not at all a mystery, it lies in the t–J Hamiltonian without frills. I have spared you these, since they are mostly of sociological interest in the long run. The present paper was the historical introduction, which summarizes much of this agonizing reappraisal, to a longer unfinished version which may never see the light of day. Then I will follow with a couple of papers which present some fresh ideas I came upon…

no commentary…

no commentary…

A plenary talk for the fourth of the “Kyoto” international theoretical physics congresses, in a very hot Paris summer of 2002 — well, Kyoto 1953 was hotter even than that, after all. I burden you with it because it contains some meat in the form of my reappraisal of the entire field of post-BCS superconductors…

I realized that the old Gutzwiller-Hubbard approach as applied in 1988 by a group under Rice, and much later refined by Randeria et al., could answer conclusively most of the questions one might want to ask, including about spin-charge separation, and began gathering as many of the participants in this development as possible to write up a summary of what this method could do, hoping thereby to convince at least a fair selection of experimentalists that we have the basic ideas right. This paper is the result. Still more is to come, I'm sure, along the same lines — it seems to work better than it reasonably should, for many low-temperature phenomena. As I kept desperately insisting for these 15 years, high-T_c superconductivity is NOT a mystery…