Non-equilibrium steady states for the interacting Klein-Gordon field in 1+3 dimensions

TL;DR

This paper extends the analysis of non-equilibrium steady states (NESS) in quantum field theory, specifically for the interacting Klein-Gordon field in 1+3 dimensions, using algebraic and perturbative methods to explore their properties.

Contribution

It generalizes previous results for free fields to interacting models, incorporating chemical potentials, condensates, and smooth contact transitions within an algebraic QFT framework.

Findings

Interacting NESS exhibit thermodynamic properties similar to linear models.

Perturbation theory cannot fully describe thermalization in non-linear QFT.

Interacting NESS are stable under small perturbations.

Abstract

Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolution of two infinite heat baths brought into thermal contact. In this work we generalise corresponding results of Doyon~et.~al. (J.\ Phys.\ A 18 (2015) no.9) for free Klein-Gordon fields in several directions. Our analysis is carried out directly at the level of correlation functions and in the algebraic approach to QFT. We discuss non-trivial chemical potentials, condensates, inhomogeneous linear models and homogeneous interacting ones. We shall not consider a sharp contact at initial time, but a smooth transition region. As a consequence, the states we construct will be of Hadamard type, and thus sufficiently regular for the perturbative treatment of interacting models. Our analysis shows that perturbatively constructed interacting NESS display thermodynamic properties similar to the ones of the NESS in linear models. In particular, perturbation theory appears to be insufficient to describe full thermalisation in non-linear QFT. Notwithstanding, we find that the NESS for linear and interacting models is stable under small perturbations, which is one of the characteristic features of equilibrium states.