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

Authors: Kamenev, Alex; Levchenko, Alex

Source: Advances In Physics, Volume 58, Number 3, May 2009 , pp. 197-319(123)

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Abstract:

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 the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc.

Keywords: Keldysh technique; Green's functions; kinetic equation; non-linear σ-model; mesoscopic systems; fluctuating superconductors

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00018730902850504

Affiliations: 1: Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA

Publication date: 2009-05-01

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