Memory effects upon the relaxation dynamics of the Wigner distribution function

Abstract

The solutions of the generalized Fokker-Planck equation that arises in the semiclassical description of a quantal harmonic coordinate immersed in an arbitrary heat bath are investigated in the non-Markovian regime. The treatment consists of retaining a finite number of terms of the analytic expansion of the Laplace-transformed memory kernel around the origin which leads to approximate relaxation frequencies involving different degrees of memory. For a regime of highly inelastic collisions the authors extend previous findings concerning the relation between Markovian and non-Markovian relaxation frequencies and, for the usual elastic coupling, they consider fermion and phonon environments showing that the former involves a much more complex dynamics with a non-exponential time decay. Focusing upon the exponential part of the decay, they find that for both classes of reservoirs the first two non-Markovian corrections have well defined signs that increase the relaxation frequencies.