Derivation of non-Markoffian transport equations for trapped cold atoms in nonequilibrium thermal field theory

TL;DR

This paper derives non-Markoffian transport equations for trapped cold Bose atoms using nonequilibrium thermal field theory, capturing effects beyond traditional Markovian approximations, especially relevant for systems with Bose-Einstein condensates.

Contribution

It introduces a self-consistent derivation of non-Markoffian transport equations for both condensed and non-condensed cold atoms within thermal field theory, including a new collision term for condensates.

Findings

Derived non-Markoffian transport equations at two-loop level.

Reduced non-Markoffian equations to quantum Boltzmann form in Markovian limit.

Identified a new collision term relevant for Landau instability in condensates.

Abstract

The non-Markoffian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal filed theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markoffian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markoffian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.