Keldysh technique and non-linear sigma-model: basic principles and applications

Details Keldysh technique and non-linear sigma-model: basic principles and applications Keldysh technique and non-linear sigma-model: basic principles and applications

2009-01-23

arxiv.org/abs/0901.3586v3

Advances in Physics 58, 197 (2009)

Physics

Condensed Matter

Other Condensed Matter

Review: 103 pages, 19 figures

Scientific paper

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear sigma-model for disordered metals and superconductors. We discuss such topics as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equation, etc. The sections devoted to disordered superconductors include Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a substantial extension of arXiv:cond-mat/0412296.)

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