Wikinventia — Atlas of discoveries and inventions · Global Age

Microscopic derivation of Fermi liquid theory — Nozières and Luttinger

1962 AD · Transmission: Global
PhysicsTheoryNorth American

Between 1956 and 1959, Lev Landau had proposed in the USSR a radical phenomenological theory: a system of electrons repelling each other with intense force inside a metal could, under certain conditions, behave as if made of nearly free particles — "quasiparticles" — with an effective mass renormalized by the interactions. Landau's proposal was a physically brilliant hypothesis but built by analogy with an ideal gas, with no justification starting directly from the principles of many-body quantum mechanics: it was unknown whether the scheme was a useful approximation or a necessary consequence of quantum field theory applied to a system of interacting fermions. Philippe Nozières, trained under David Pines at Princeton and influenced by the group of Bell Labs theorists during his summer visits, resolved that gap in 1962 together with Joaquin Mazdak Luttinger, of Columbia University, in work published in two consecutive parts in Physical Review. Using the Feynman-diagram and Green's-function formalism — the same technical apparatus of quantum electrodynamics, here applied to a many-body solid-state system — Nozières and Luttinger showed that a broad class of Landau's theoretical conclusions could be rigorously derived within many-body perturbation theory, including the case of long-range Coulomb forces, and obtained a general expression for the quasiparticle distribution function Landau had postulated. The work turned a brilliant phenomenological intuition into a theorem provable from first principles, and is the formal basis on which today rests all the physics of conventional metals, liquid helium-3, and, more recently, much of the theory of correlated quantum materials.

InstitutionColumbia University
Historical regionUnited States
Primary sourceNozières, P., Luttinger, J. M. — "Derivation of the Landau Theory of Fermi Liquids. I. Formal Preliminaries" (Physical Review, 127(4), 1423-1431, 1962). DOI: 10.1103/PhysRev.127.1423. Luttinger, J. M., Nozières, P. — "...II. Equilibrium Properties and Transport Equation" (Physical Review, 127(4), 1431-1440, 1962). DOI: 10.1103/PhysRev.127.1431
Secondary sourceWolf Prize — Physics 1985 — Press release (wolffund.org.il/philippe-nozireres); on Landau's theoretical precedent: L. D. Landau, "The Theory of a Fermi Liquid", Soviet Physics JETP 3(6), 920-925, 1956 — already documented in the corpus as part of Landau's legacy (see landau-condensed-matter-1941, ginzburg-landau-superconductivity-1950)
Original languageEnglish
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