Quantum kinetic equations, memory effects, conservation laws

Abstract

In the framework of real-time Green's functions, a general non-Markovian Boltzmann equation including initial correlations, full time retardation (memory) and self energy is considered. This equation conserves the total (kinetic plus potential) energy. Two approximations of this very general equation are investigated: (i) the first order expansion with respect to the retardation and (ii) the first Born approximation for the scattering T-matrix (non-Markovian Landau equation). The influence of memory and damping effects on the relaxation of the one-particle distribution and of the kinetic energy is demonstrated by a numerical analysis.