Repelling Random Walkers in a Diffusion-Coalescence System

TL;DR

This paper analyzes a one-dimensional diffusion-coalescence system, showing how shock structures perform biased random walks and how the system's phases affect shock separation.

Contribution

It introduces a superposition of double shock structures to describe the steady state and characterizes phase-dependent shock behavior.

Findings

Mean shock distance is proportional to system size in one phase.

Shock structures perform biased random walks with repulsion.

System exhibits two distinct phases based on reaction rates.

Abstract

We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double shock structures which perform biased random walks on the lattice while repelling each other. The shocks can enter into the system and leave it from the boundaries. Depending on the microscopic reaction rates, the system is known to have two different phases. We have found that the mean distance between the shock positions is of order L in one phase while it is of order 1 in the other phase.