Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics

TL;DR

This paper presents an exact analytical method for solving diffusion-limited reactions with synchronous dynamics on a 1D lattice, revealing detailed temporal behaviors and scaling laws.

Contribution

Introduces a novel exact solution approach for reactions with synchronous particle hopping, linking densities and correlations at all times.

Findings

Exact relations between densities and correlations are established.

Asymptotic behaviors at large times are explicitly derived.

Scaling laws for low initial densities are formulated.

Abstract

A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and certain correlation properties of these two reactions at all times. Asymptotic behavior at large times as well as scaling form describing the regime of low initial density, are derived explicitly.