Ergodicity breaking in one-dimensional reaction-diffusion systems

TL;DR

This paper studies one-dimensional reaction-diffusion systems with particle creation and annihilation, revealing conditions for ergodicity breaking and metastability, supported by analytical and Monte Carlo simulation results.

Contribution

It provides a simple criterion for ergodicity breaking in driven diffusive systems with bulk reactions, and analyzes the metastable states and their lifetimes.

Findings

Existence of non-ergodic phase with multiple stationary states

Metastable states have exponentially large lifetimes in system size

Monte Carlo simulations confirm analytical predictions

Abstract

We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems can exhibit ergodicity breaking in the thermodynamic limit. The triggering mechanism is the random motion of a shock in an effective potential. Based on this physical picture we provide a simple condition for the existence of a non-ergodic phase in the phase diagram of such systems. In the thermodynamic limit this phase exhibits two or more stationary states. However, for finite systems transitions between these states are possible. It is shown that the mean lifetime of such a metastable state is exponentially large in system-size. As an example the ASEP with the A0A--AAA reaction kinetics is analyzed in detail. We present a detailed discussion of the phase diagram of this particular model which indeed exhibits a phase with broken ergodicity. We measure the lifetime of the metastable states with a Monte Carlo simulation in order to confirm our analytical findings.