Statistical Physics (Ph.D.)

Statistical Physics (Ph.D.) (Fall '24)


Text and reference books: mainly the Statistical Physics textbooks by Mehran Kardar [K] and by Kerson Huang [H] and by Pathria [P] (going back and forth). An excellent classic overall and for various subtopics is vol.5 (Stat.Phys.) of Landau-Lifshitz Course in Theoretical Physics series. Outline of contents:

Global picture of evolution of macroscopic systems: nonlinear dynamics, 1-d and 2-d systems, fixed points, flowlines, population growth, Lotka-Volterra model etc [Strogatz "Nonlinear dynamics and chaos", ch.5, sec.6.1-6.4, sec.2.3].

Generalities on classical statistical physics, probabilistic approaches [K 4.1]; Microcanonical ensemble, 2-level systems, the ideal gas, mixing entropy [K 4.2-4.5]; Canonical ensemble, standard examples; Grand canonical ensemble.

Including interactions, perturbation theory; the virial expansion and van der Waals equation [K 5.1-5.3]; Condensation, mean field theory, liquid-gas transition [K 5.5].

Quantum statistical mechanics: examples -- dilute gases, vibrations in solids, phonons, specific heat [K 6.1-6.2]; very quick overview of blackbody radiation and the Planck resolution of the ultraviolet catastrophe [K 6.3]; quantum macrostates and the density matrix [K 6.5].

Ideal quantum gases and identical particles [K ch.7]: generalities [K 7.1]; grand canonical formulation [K 7.3]; nonrelativistic gases, high temperature limit [K 7.4]; degenerate Fermi gas [K 7.5]; degenerate Bose gas and Bose-Einstein condenation [K 7.6].

* takehome midsem, endsem, assignment

Suggested follow-up reading:

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