Creation-annihilation processes in the ensemble of constant particle number

TL;DR

This paper investigates creation-annihilation processes in a fixed-particle ensemble, analyzing how clusters are annihilated and particles are catalytically created, with numerical studies on models related to contact processes.

Contribution

It introduces a framework for studying creation-annihilation dynamics in a constant particle number ensemble and demonstrates how to derive this from the constant rate ensemble.

Findings

Numerical analysis of three nonequilibrium models with cluster annihilation.

Method to construct constant particle number ensemble from constant rate ensemble.

Insights into the behavior of conserved cluster annihilation processes.

Abstract

We study, in the ensemble of constant particle number, processes in which a cluster of particles is annihilated and particles are created catalytically in active sites. In this ensemble, particles belonging to a cluster of $\ell$ particles jump to $\ell$ distinct active sites. As examples of our prescription, we analyze numerically three nonequilibrium systems that annihilate cluster of particles that are identified as conserved versions of the pair annihilation contact model, triplet annihilation contact model and pair contact process. We show also how to set up the constant particle number ensemble from the constant rate ensemble.