2004 FEENBERG MEDAL CITATION: Spartak T. Belyaev and Lev P. Gor'kov

In the late fifties Russian theorists were among the first to use field theoretical methods borrowed from quantum electrodynamics in the field of Statistical Physics. A series of landmark papers applied them to a wide variety of problems. Some of them were also conceptual breakthroughs. The papers of Spartak Belyaev and Lev Gor'kov belong to that very special class.

Spartak Belyaev was born in 1924. Just out of high school, he served in the Russian Army during World War II, from 1941 to 1946. Upon release, he went to Moscow State University and soon started research with G.E. Budker on relativistic kinetic equations in plasmas. In 1949, he realized that his interests were in theory and he joined the group of Arkady Migdal. The road was then wide open! He joined the Kurtchatov Institute in 1952, and received his Doctorate of Science in 1962. His fame spread quickly. He was invited to the Niels Bohr Institute in 1957-1958, and delivered two famous courses at the 1958 Les Houches school on many body problems.

He left Moscow in 1962 for Novosibirsk, where a major research center was being built. He created an outstanding theory group at the Budker Institute of Nuclear Physics. He also served as rector of the University and was influential in making Novosibirsk a success. After 1978, he returned to the Kurtchatov Institute in Moscow, and eventually became the director of the Institute of General and Nuclear Physics. He is largely responsible for maintaining the high level of the Kurtchatov Institute throughout the difficult times of the 90's. Being a man of great civic, as well as scientific responsibility, he was deeply involved in the assessment of the Chernobyl disaster. He was elected to the Russian Academy of Sciences as a correspondent in 1964 and as a full member in 1968. He received the Landau gold medal in 1998.

Lev Gor'kov was born in 1929. He studied engineering at the Moscow State University and was one of the first graduates of the "Moscow Mechanical Institute" that had just been created for outstanding students. He joined the theory group of Lev Landau at the Institute of Physical Problems, together with Abrikosov, Dzyaloshinski and the more senior Khalatnikov. The quartet was destined to become the core of the Landau Institute. He received his Doctorate of Science in 1960 in Leningrad. After the death of Landau, a new "Landau Institute for Theoretical Physics" was created in Chernogolovka, and Gor'kov stayed there until 1992, eventually serving as the deputy director.

He left Moscow in 1992 for United States, where he settled in Tallahassee in the National High Magnetic Field Laboratory at Florida State University. Through the years, he received many distinctions. He was elected to the Russian Academy of Sciences as a correspondent in 1966, and as a full member in 1987. He received the Lenin award for Physics in 1966, the Landau award in 1988, and the Bardeen award in 1991.

In 1957, superfluidity and superconductivity were understood in the context of elementary methods that turned out to correspond to mean field theory. The 1949 paper of of Bogoliubov explained elementary excitations and condensate depletion in He4 and the brand new BCS theory accounted for equilibrium and near equilibrium properties of superconductors. However, one could not go further without a full theoretical framework, and Belyaev and Gor'kov extablished that framework. They realized that the symmetry breaking of a superfluid allows conversion of a particle into a hole. As a result, an anomalous propagator appears, which describes coherent pair exchange with the condensate. Once that coherent coupling of particles was put into the theory, all the machinery of perturbation theory was available, with a slightly more complicated algebra. One could approach all sorts of previously inaccessible problems. Their papers appeared a few months apart and each of them opened a whole field. Belyaev came first. He dealt with bosons and was able to push the Bogoliubov calculation to next order in a density expansion. It was a real "tour de force" where he had to sidestep all sorts of divergences. Beyond the technical aspects of his achievement, the next order changed the physics. Discrete quasiparticle modes were now hybridized with a continuum of multiparticle states and any discrete mode lying inside that continuum was broadened, acquiring a finite lifetime. Along the way, Belyaev noted that the condensate dynamics is controlled by the chemical potential, a remark which would bloom in the Josephson effect. Of course, second order does not tell us everything, and for 30 years Belyaev's calculation remained a major conceptual step without much experimental relevance. However, the recent discovery of Bose Einstein condensation in trapped alkali gases has put his work back on the front line: his density expansion is just what is needed for such dilute systems.

Gor'kov used a similar approach for superconductors. The BCS wave function implies a coherent hybridization of singlet pairs (k,-k), which are naturally described with the same anomalous propagators. Gorkov thus cast the theory in a very elegant form, which nowadays is a universally accepted common language. More importantly, the formalism is flexible enough to allow for more complicated situations. Having established the language, Gor'kov embarked on a series of applications, each of which turned out to be a major breakthrough. He first extended the theory to spatially inhomogeneous systems, providing a detailed microscopic derivation of the famous Ginzburg-Landau phenomenological equations. In this way he could explain the microscopic meaning of the coefficients that enter that equation. Together with Abrikosov, he applied it to dirty systems, where ordinary pairing of plane waves does not hold. They showed that scalar impurities have little effect on superconductivity, a surprising far-reaching conclusion arising from the fact that pairing involves time reversed states that ignore translational invariance. In contrast, magnetic impurities are lethal, destroying the pairs as soon as the mean free path is comparable to the pair radius. Pushing that analysis further they discovered "gapless superconductivity" by showing that impurities can close the gap without killing superconductivity. Finally, Gor'kov and Eliashberg devised a theory of non-equilibrium superconductivity, opening an important new field. The heritage of anomalous propagators is truly impressive.

Besides this seminal work, both Belyaev and Gor'kov blossomed with new ideas throughout their careers. Shortly after his work on dilute Bose liquids, when he went to Copenhagen, Belyaev'ss interests moved to nuclear theory. He was extremely influential in understanding the role of pairing in finite nuclei, and studied moments of inertia, quadrupole deformations, vibrations related to zero sound, and related phenomena. He also developed a consistent theory of correlations beyond the random phase approximation. Gor'kov quickly became a leading authority in solid state theory. One can hardly choose between all his groundbreaking papers. Several highlights include his work with Bychkov on de Haas van Alphen oscillations in an interacting Fermi liquid, his work with Bychkov and Dzyaloshinski on the competition between superconductivity and charge density waves in one-dimensional chains, and his work with Volovik on anisotropic superconductors.

Spartak Belyaev and Lev Gor'kov have left a lasting imprint on many body theory. Either of them would separately deserve the Feenberg medal. Honoring them jointly emphasizes both the the deep connection of their work, and the extraordinary vitality of Russian theoretical physics in the 1960's.


SELECTION COMMITTEE

The selection committee included Charles Campbell of University of Minnesota, John W. Negele of MIT, chair, and the previous Feenberg Medal recipient, Philippe Nozieres of the Institute Laue-langevin in Grenoble.

THE FEENBERG MEMORIAL MEDAL

The Eugene Feenberg Memorial Medal was established in 1983 by the many-body physics community in memory of the unique and enduring contributions of Eugene Feenberg to physics, especially to the foundations of nuclear physics and microscopic quantum many-body physics of nuclei and quantum fluids. The medal is presented under the auspices of the International Advisory Committee for the Series of International Conferences on Recent Progress in Many-Body Theories at meetings in that series. Previous recipients are David Pines (1985), John W. Clark (1987), Malvin H. Kalos (1989), Walter Kohn (1991, 1998 Nobel laureate), David M. Ceperley (1994), Lev P. Pitaevskii (1997), Anthony J. Leggett (1999, 2003 Nobel laureate), and Philippe Nozieres (2001).

Born October 19, 1906 in Fort Smith, Arkansas, Eugene Feenberg received a B.A. in physics and M.A. in mathematics in 1929 from the University of Texas, Austin after three years of study. After a year and a half traveling in Europe as a Parker Traveling Fellow, visiting the groups of Sommerfeld, Pauli, and Fermi, he received his Ph.D. in 1933 from Harvard University, where his thesis advisor was E. C. Kemble. His thesis included the first statement and proof of the quantum optical theorem. 

Subsequently Feenberg was Instructor or Fellow at Harvard, Wisconsin, and the Institute for Advanced Studies, during which time he collaborated with Wigner, Bardeen, Breit and Phillips among others. After eight years on the faculty of New York University and four years during World War II at Sperry Gyroscope, Feenberg joined the faculty of Washington University (St. Louis) in 1946, and in 1964 became the Wayman Crow Professor of Physics, a chair previously held by Arthur H. Compton, Arthur L. Hughes, and Edward U. Condon. 

Much of Feenberg's early research was concerned with the theory of the nucleus, culminating in the publication of "Shell Theory of the Nucleus" by Princeton University Press in 1955. While he had a career-long interest in perturbation theory, he turned his primary focus to the theory of quantum fluids, most notably the helium liquids, toward the end of the 1950's, a subject to which he would contribute very importantly for the next two decades until his death in 1977 . Along with his students, he developed the method of correlated basis functions in order to deal with the strong, short-range repulsion between helium atoms that makes the theory of the helium fluids virtually intractable using ordinary perturbation theory. The early part of this research is the subject of his monograph "Theory of Quantum Fluids" (Academic Press, 1969).

His willingness to tackle the challenge of strong, short-range correlations by developing a theoretical, ab initio framework to deal with them from first principles, characterizes much of Feenberg's research. As important as his research is, his personal integrity and high principles continue to serve as an inspiration for his former students and colleagues. The awarding of the Eugene Feenberg Memorial Medal serves as an opportunity to commemorate and perpetuate this man's unique influence on physics and physicists.