Non-Equilibrium Diagram Technique

Abstract

The description of transport phenomena under conditions far from equilibrium requires a more careful consideration for the systems with strong scattering, since both the reconstruction of energy spectrum and the distribution of quasiparticles have to be considered simultaneously. For these purposes, it is convenient to use the nonequilibrium diagram technique, which operates, apart from the retarded and advanced Green’s functions, with an additional function determining non-equilibrium distribution of the quasiparticles. The one-electron formulation of this technique, given below for the electron-impurity system, is a generalization of the kinetic description developed in Chapter 2 for the case of weak scattering. The non-equilibrium diagram technique (NDT) allows one to derive kinetic equations for describing the response of a system to external fields (not necessarily in the linear regime) in a unified way, by considering the series of diagrams with a required accuracy with respect to the interaction. In this way one can describe, for example, the systems of interacting electrons and the interacting electron-phonon systems, which cannot be treated diagrammatically at non-zero temperature with the use of the technique given in Chapter 3. Since the applications of the NDT often require a complex and lengthy consideration, below we present only a limited number of examples of this kind.