Keldysh technique and non-linear-model: Basic principles and applications

Alex Kamenev, Alex Levchenko

Research output: Contribution to journalArticlepeer-review

258 Scopus citations


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-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.

Original languageEnglish (US)
Pages (from-to)197-319
Number of pages123
JournalAdvances in Physics
Issue number3
StatePublished - May 2009


  • Fluctuating superconductors
  • Green's functions
  • Keldysh technique
  • Kinetic equation
  • Mesoscopic systems
  • Non-linear-model


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