Exact dynamics of a reaction-diffusion model with spatially alternating rates

TL;DR

This paper provides an exact solution for the full dynamics of a nonequilibrium spin chain and its reaction-diffusion dual, revealing how alternating rates and negative temperatures influence decay and oscillations in observables.

Contribution

It introduces an exact analytical solution for a reaction-diffusion model with spatially alternating rates and explores the effects of negative temperatures on system dynamics.

Findings

Exponential decay to steady state when both temperatures are positive.

Damped oscillations occur if one temperature is negative.

Competition between pair creation and annihilation causes oscillations.

Abstract

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative ``temperatures'' have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time-dependence are found: if both temperatures are positive, the magnetization, density and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.