Particle Dynamics in a Mass-Conserving Coalescence Process

TL;DR

This paper analyzes a one-dimensional mass-conserving coalescence process with biased particle movement, providing exact solutions and a scaling theory that enhance understanding of particle correlations and dynamics.

Contribution

It introduces an exact mapping to a ballistic surface deposition model and develops a comprehensive scaling theory for the mass-conserving coalescence process.

Findings

Exact mass-mass correlation functions obtained.

Scaling theory validated by analytical and numerical results.

Enhanced understanding of particle dynamics in mass-conserving systems.

Abstract

We consider a fully asymmetric one-dimensional model with mass-conserving coalescence. Particles of unit mass enter at one edge of the chain and coalescence while performing a biased random walk towards the other edge where they exit. The conserved particle mass acts as a passive scalar in the reaction process $A+A\to A$, and allows an exact mapping to a restricted ballistic surface deposition model for which exact results exist. In particular, the mass- mass correlation function is exactly known. These results complement earlier exact results for the $A+A\to A$ process without mass. We introduce a comprehensive scaling theory for this process. The exact anaytical and numerical results confirm its validity.