Many-body theory of non-equilibrium systems

TL;DR

This paper provides an introduction to the Keldysh formalism within the functional integral framework, covering topics like kinetic theory, classical relations, and disordered fermions for non-equilibrium quantum systems.

Contribution

It offers a comprehensive lecture-based overview of non-equilibrium many-body theory using the Keldysh formalism, connecting it with classical techniques and disordered systems.

Findings

Introduction to Keldysh formalism for bosons and fermions

Connection between quantum kinetic theory and classical methods

Application of non-linear sigma model to disordered fermions

Abstract

Lectures notes for 2004 Les Houches Summer School on "Nanoscopic Quantum Transport". These lectures contain an introduction to Keldysh formalism for interacting bosonic and fermionic systems, presented in the functional integral framework. Covered topics include: kinetic theory, relation to classical techniques (such as Martin--Siggia--Rose and Fokker--Planck), non--linear sigma model for disordered fermions, etc.