Nonequilibrium Dynamics of Scalar Fields in a Thermal Bath

TL;DR

This paper investigates how scalar fields coupled to a thermal bath approach equilibrium, analyzing the dynamics through Kadanoff-Baym equations and comparing results with Boltzmann equations to understand the validity of approximations.

Contribution

It demonstrates the equivalence of Kadanoff-Baym equations to a stochastic Langevin equation and explores the temperature-dependent spectral density in scalar field thermalization.

Findings

Spectral density depends on decay, inverse decay, and Landau damping.

Equilibrium properties are determined by Bose-Einstein distribution at a complex pole.

Boltzmann approximation validity depends on initial conditions and interaction range.

Abstract

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.