Fluctuations and the role of collision duration in reaction-diffusion systems

TL;DR

This paper investigates how fluctuations and collision durations influence the steady-state behavior of reaction-diffusion systems, highlighting the importance of collision time statistics through simulations and theoretical analysis.

Contribution

It introduces the role of collision duration statistics as a key factor in reaction-diffusion systems and provides approximate formulas for densities and critical diffusion coefficients.

Findings

Collision duration significantly affects steady-state statistics.

Approximate expressions for species densities are derived.

Critical diffusion coefficients are identified for system sustainability.

Abstract

In a reaction-diffusion system, fluctuations in both diffusion and reaction events, have important effects on the steady-state statistics of the system. Here, we argue through extensive lattice simulations, mean-field type arguments, and the Doi-Peliti formalism that the collision duration statistics -- i.e., the time two particles stay together in a lattice site -- plays a leading role in determining the steady state of the system. We obtain approximate expressions for the average densities of the chemical species and for the critical diffusion coefficient required to sustain the reaction.