Time Reversal and Many-Body Non-equilibrium Green Functions

A. V. Koshelkin

A. V. Koshelkin

ZHOU GUANG-ZHAO, Zhao-Bin Su, 中国科学院理论物理研究所

This is the first part of our work on time reversal symmetry applied to non-equi-librium statistical stationary states from a unified microscopic quantum statistical point of view. In this paper, a formalism for time reversal symmetry is constructed in the framework of the Closed Time Path Green's Functions (CTPGF), which can be applied both to equilibrium and non-equilibrium stationary states. By using the generating functional technique of the CTPGF, symmetry relations for the statistical Green's functions and vertex runctions are derived for systems invariant under time reversal.

Bich Ha Nguyen

In the quantum field theory with the vacuum being the ground state the Green functions are the vacuum expectation values of the chronological, retarded or advanced products of the field operators (Bjoken & Drell, 1964; Itzykson & Zuber, 1985; Peskin & Schroeder, 1995). They are the generalized functions of the real time variables ti (and also other spatial coordinates). For the application of the Green function technique to the study of the timeindependent phenomena in equilibrium many-body systems at a finite temperature, the Matsubara imaginary time Green functions were introduced and widely used (Abrikosov et al., 1975; Bruuns & Flensberg, 2004; Haken, 1976). They are the mean values over a statistical ensemble at a finite temperature of the chronological products of the imaginary timedependent operators. Both these types of Green functions are inadequate for the application to the study of the time-dependent phenomena in the many-body systems with a finite density and at a finite temperature, in particular the non-equilibrium systems. For the application to the study of the time-dependent dynamical processes in non-equilibrium many-body systems Keldysh (Keldysh, 1965) has introduced a more general class of timedependent Green functions at finite temperature and density. They are the mean values of the time-ordered products of quantum operators in the Heisenberg picture over statistical ensembles of many-body systems with finite densities and at finite temperatures (which may be non-vanishing). The simplest example is the two-point Green function

Thomas Gasenzer, Stefan Keßler, Jan Martin Pawlowski