Thermalization with non--zero initial anomalous quantum averages

TL;DR

This paper investigates how non-zero initial anomalous quantum averages influence thermalization in a scalar field theory, showing analytically that these averages decay to zero and no equilibrium with non-zero averages exists.

Contribution

It derives kinetic equations for level populations and anomalous averages in a scalar field theory, revealing their relaxation behavior and absence of non-zero equilibrium states.

Findings

Anomalous averages relax to zero over time.

No equilibrium state with non-zero anomalous averages exists.

Analytical demonstration in the linear approximation.

Abstract

We discuss the thermalization process in the kinetic approximation in the presence of non--zero initial anomalous quantum expectation values on top of an initial non--planckian (non--thermal) level population. Namely we derive a system of "kinetic" equations for the level population and anomalous expectation values in four--dimensional massive scalar field theory with $\varphi^4$ self--interaction. We show analytically in the linear approximation that for their small initial values the anomalous quantum averages relax down to zero. Furthermore, we show analytically that this system does not have an equilibrium solution with non--zero time independent anomalous expectation value.