Retarded versus Time-Nonlocal Quantum Kinetic Equations

Abstract

The finite duration of the collisions in Fermionic systems as expressed by the retardation time in non-Markovian Levinson-type kinetic equations is discussed in the quasiclassical limit. We separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates, (iii) renormalization of the single-particle energy, (iv) collision delay, and (v) related nonlocal corrections to the scattering integral. In this way we transform the Levinson equation into the Landau–Silin equation extended by the nonlocal corrections known from the theory of dense gases. The derived nonlocal kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other.