Non-Markovian quantum kinetics and conservation laws

TL;DR

This paper explores how memory effects influence quantum kinetic equations and their relation to energy conservation, deriving equations that incorporate correlations and ensure energy conservation in nonequilibrium quantum systems.

Contribution

It introduces a kinetic framework that explicitly links non-Markovian memory effects with energy conservation through nonequilibrium correlations, using the density operator method.

Findings

Derivation of a non-Markovian quantum kinetic equation with correlation contributions.

Demonstration that the correlation term cancels the collision term at thermal equilibrium.

Explicit expressions for entropy production and correlation energy in non-Markovian regimes.

Abstract

A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction energy. The kinetic equation contains a correlation contribution which exactly cancels the collision term in thermal equilibrium and ensures the energy conservation in nonequilibrium states. Explicit expressions for the entropy production in the non-Markovian regime and the time-dependent correlation energy are obtained.