{"title":"Keldysh technique and non-linear σ-model: basic principles and applications","authors":"A. Kamenev, A. Levchenko","doi":"10.1080/00018730902850504","DOIUrl":null,"url":null,"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.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":null,"pages":null},"PeriodicalIF":35.0000,"publicationDate":"2009-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730902850504","citationCount":"296","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1080/00018730902850504","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
引用次数: 296
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.
期刊介绍:
Advances in Physics publishes authoritative critical reviews by experts on topics of interest and importance to condensed matter physicists. It is intended for motivated readers with a basic knowledge of the journal’s field and aims to draw out the salient points of a reviewed subject from the perspective of the author. The journal''s scope includes condensed matter physics and statistical mechanics: broadly defined to include the overlap with quantum information, cold atoms, soft matter physics and biophysics. Readership: Physicists, materials scientists and physical chemists in universities, industry and research institutes.