Cluster approximation solution of a two species annihilation model

TL;DR

This paper analyzes a one-dimensional two-species annihilation model, solving mean field equations exactly and exploring cluster mean field approximations to understand long-term behavior based on diffusion rates.

Contribution

It provides an exact solution for mean field equations and investigates cluster mean field approximation, highlighting the influence of diffusion rates on asymptotic behavior.

Findings

Large time behavior depends on diffusion rates

Mean field equations solved exactly

Cluster approximation studied

Abstract

A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved exactly. Cluster mean field approximation of the model is also studied. It is shown that, the general form of large time behavior of one- and two-point functions of the number operators, are determined by the diffusion rates of the two type of species, and is independent of annihilation rates.