Perturbation theory for a non-equilibrium stationary state of a one-dimensional stochastic wave equation

TL;DR

This paper develops a perturbative approach to construct and analyze the non-equilibrium stationary state of a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, including renormalization effects.

Contribution

It introduces a novel perturbation theory framework for non-linear stochastic wave equations, incorporating a renormalized potential determined by a fixed point equation.

Findings

Explicit low-order two-point function calculations

Identification of the renormalized potential in the linearized theory

Framework for systematic perturbative analysis of non-equilibrium states

Abstract

We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear equations of motion including an additional potential term which emerges in the renormalization of the perturbation expansion for the state corresponding to the non-linear equations of motion. The potential is the solution to a fixed point equation. Low order terms in the expansion for the two-point function are determined.