Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A

TL;DR

This paper provides an exact analytical solution for the entire hierarchy of correlation functions in the one-dimensional diffusion-limited coalescence process, advancing the understanding of such reaction systems.

Contribution

It derives the first complete exact description of all correlation functions for the A + A -> A process in one dimension.

Findings

Exact hierarchy of correlation functions obtained

Full characterization of the particle system achieved

Advances the analytical understanding of diffusion-limited reactions

Abstract

Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the distribution of distances between nearest particles. However, a full characterization of a particle system is only provided by the infinite hierarchy of multiple-point density correlation functions. We derive an exact description of the full hierarchy of correlation functions for the diffusion-limited irreversible coalescence process A + A -> A.