Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains

TL;DR

This paper establishes a method to analyze one-dimensional reaction-diffusion systems by mapping them onto integrable quantum chains, enabling exact calculations of their time-dependent properties and identifying new related stochastic processes.

Contribution

It introduces a novel approach to study reaction-diffusion models via integrable quantum chains and classifies free fermion systems with site-independent interactions.

Findings

Exact time-dependent mean particle density calculations

Identification of new integrable stochastic processes related to the XXZ chain

Determination of relaxation times for particle density and correlations

Abstract

One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The reaction-diffusion processes related to free fermion systems with site-independent interactions are classified. The time-dependence of the mean particle density is calculated. Furthermore new integrable stochastic processes related to the Heisenberg XXZ chain are identified and the relaxation times for the particle density and density correlation for these systems are found.