Field Theory of Propagating Reaction-Diffusion Fronts

TL;DR

This paper develops an analytic field-theoretic framework to understand the velocity selection of reaction-diffusion fronts, bridging fundamental principles with effective equations and confirming results through simulations.

Contribution

It introduces a novel field-theoretic approach to reaction-diffusion front velocity selection, incorporating fluctuations beyond mean field theory.

Findings

Analytic theory matches numerical simulation results

Connects reaction-diffusion dynamics to effective equations

Advances understanding of fluctuation effects in front propagation

Abstract

The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at the results already confirmed by numerical simulations.