Velocity and diffusion coefficient of $A+A\leftrightarrow A$ reaction fronts in one dimension

TL;DR

This paper investigates the dynamics of reaction fronts in a one-dimensional reversible A + A <-> A system, focusing on velocity and diffusion, and introduces a master equation approach considering correlated random walks of the leading particle.

Contribution

It extends the leading particle concept to a master equation framework, improving estimates of front speed and accounting for correlations in the particle's motion.

Findings

The leading particle performs a correlated random walk.

Correlation effects are essential for accurate diffusion coefficient estimates.

The method refines previous front speed calculations.

Abstract

We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get correct value of the front diffusion coefficient.