Solution of a One-Dimensional Reaction-Diffusion Model with Spatial Asymmetry

TL;DR

This paper analyzes a one-dimensional reaction-diffusion model with directional bias, providing an exact solution for the spectrum and revealing phase transitions based on asymmetry levels.

Contribution

It introduces a solvable model with spatial asymmetry, deriving the spectrum and analyzing phase behavior, which advances understanding of asymmetric reaction-diffusion systems.

Findings

Exact solution for the relaxational spectrum

Identification of two distinct phases based on asymmetry

Analysis of stationary properties in different phases

Abstract

We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be completely solvable if all processes have the same asymmetry. The relaxational spectrum is obtained directly from $H$ and via the equations of motion for strings of empty sites. The structure and the solvability of these equations are investigated in the general case. Two phases are shown to exist for small and large asymmetry, respectively, which differ in their stationary properties.