2PI nonequilibrium versus transport equations for an ultracold Bose gas

TL;DR

This paper compares the full dynamical equations from the 2PI effective action with kinetic Boltzmann equations for an ultracold 1D Bose gas, showing when kinetic descriptions with memory effects become valid.

Contribution

It demonstrates the conditions and time scales under which a non-Markovian kinetic approximation accurately describes the nonequilibrium dynamics of a 1D Bose gas.

Findings

Kinetic description with memory effects becomes valid during evolution.

Time scale for kinetic validity exceeds the near-equilibrium drift period.

Fluctuation dissipation relation holds during the near-equilibrium phase.

Abstract

The far-from-equilibrium dynamics of an ultracold, one-dimensional Bose gas is studied. The focus is set on the comparison between the solutions of fully dynamical evolution equations derived from the 2PI effective action and their corresponding kinetic approximation in the form of Boltzmann-type transport equations. It is shown that during the time evolution of the gas a kinetic description which includes non-Markovian memory effects in a gradient expansion becomes valid. The time scale at which this occurs is shown to exceed significantly the time scale at which the system's evolution enters a near-equilibrium drift period where a fluctuation dissipation relation is found to hold and which would seem to be predestined for the kinetic approximation.