Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation

TL;DR

This paper provides an exact analytical solution for a one-dimensional reaction-diffusion model with particle number conservation, revealing phase transitions, explicit density profiles, and multiple decay length scales.

Contribution

The authors derive exact solutions for the canonical partition function and density profiles, uncovering phase behavior and decay scales in a reaction-diffusion model with conserved particle number.

Findings

Two distinct phases separated by a second-order transition

Exact expressions for the canonical partition function in each phase

Density profiles decay on three different length scales

Abstract

We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two different phases which are separated by a second-order phase transition. The thermodynamic behavior of the canonical partition function of the model has been calculated exactly in each phase. Density profiles of particles have also been obtained explicitly. It is shown that the exponential part of the density profiles decay on three different length scales which depend on total density of particles.