Inter-Particle Distribution Functions for One-Species Diffusion-Limited Annihilation, A+A->0

TL;DR

This paper derives the inter-particle distribution function for one-dimensional diffusion-limited annihilation using a Glauber spin approach, revealing differences from coalescence and supported by simulations.

Contribution

It provides the first exact form of the IPDF for the annihilation process, based on an innovative independence assumption validated by simulations.

Findings

IPDF for annihilation obtained analytically

Differences between annihilation and coalescence IPDFs clarified

Simulation supports the independence assumption

Abstract

Diffusion-limited annihilation, $A+A\to 0$, and coalescence, $A+A\to A$, may both be exactly analyzed in one dimension. While the concentrations of $A$ particles in the two processes bear a simple relation, the inter-particle distribution functions (IPDF) exhibit remarkable differences. However, the IPDF is known exactly only for the coalescence process. We obtain the IPDF for the annihilation process, based on the Glauber spin approach and assuming that the IPDF's of nearest-particle pairs are statistically independent. This assumption is supported by computer simulations. Our analysis sheds further light on the relationship between the annihilation and the coalescence models.