On the Langevin description of nonequilibrium quantum fields

TL;DR

This paper explores how non-equilibrium quantum scalar fields can be approximately described by a local Langevin process, analyzing conditions for validity and applications to decoherence and entropy.

Contribution

It demonstrates the formal equivalence between quantum field evolution equations and Langevin processes, identifying when a local Markovian approximation is valid in quantum field theory.

Findings

Local Markovian dynamics is valid for a finite time range.

Weak coupling is necessary for the local approximation.

The approach aids in studying decoherence and entropy production.

Abstract

We consider the non-equilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly non-local, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.