Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems

TL;DR

This paper analyzes how small perturbations affect the long-term behavior of one-dimensional single-species reaction-diffusion systems, identifying stable and unstable regions in parameter space.

Contribution

It provides a perturbative framework to classify the stability of autonomous reaction-diffusion systems against small perturbations.

Findings

Stable regions where relaxation times change continuously

Unstable regions where small perturbations drastically alter behavior

Partitioning of parameter space into stability regimes

Abstract

Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is stable against the perturbations, in the sense that largest relaxation time of the one-point functions changes continuously with perturbations. In the other part, however, the system is unstable against perturbations, so that any small perturbation drastically modifies the large-time behavior of the one-point functions.