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

TL;DR

This review provides a detailed pedagogical introduction to the Keldysh technique and non-linear sigma-model, focusing on their applications to disordered metals, superconductors, and out-of-equilibrium quantum systems.

Contribution

It offers a comprehensive derivation and application of the non-linear sigma-model within the Keldysh framework for complex disordered and superconducting systems.

Findings

Derived transport properties and mesoscopic effects in disordered systems

Analyzed interaction corrections and kinetic equations

Explored fluctuation effects in superconductors

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 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.)