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

By Alex Kamenev, Alex Levchenko. 2009

344 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6617365f5323d8f2e85374cf80381c4bc1992363

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Colloquium : Nonequilibrium effects in superconductors with a spin-splitting field (2017, background): “These concentrate on a contact interaction model and disregard self-consistent screening effects in dirty superconductors (Feigel’man et al., 2000; Kamenev and Levchenko, 2009; Narozhny et al., 1999).”
Engineered Open Systems and Quantum Simulations with Atoms and Ions (2012, background): “One prominent example is certainly electron systems in condensed matter, which are exposed to a bias voltage (Kamenev and Levchenko, 2009).”
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “…2005; Schollwöck and White, 2006; Vidal, 2003, 2004; White, 1992) and higher dimensional ones (Verstraete et al., 2008), the Keldysh technique (Kamenev and Levchenko, 2009) which is particularly helpful for deriving quantum kinetic equations, and closely related functional integral methods…”
Phase space representation of quantum dynamics (2009, methodology): “This technique is often used to derive the quantum kinetic equation and obtain single-particle distribution functions in non-equilibrium systems (Kamenev and Levchenko, 2009).”