Current fluctuations in the zero-range process with open boundaries

TL;DR

This paper investigates the long-term behavior of current fluctuations in a one-dimensional zero-range process with open boundaries, revealing site-dependent fluctuations as a precursor to condensation transitions, supported by Bethe ansatz analysis.

Contribution

It introduces the connection between current fluctuation site-dependence and condensation transition, with a novel analysis using Bethe ansatz for the exclusion process equivalent.

Findings

Current fluctuations become site-dependent above a critical current.

Site dependence of fluctuations signals an impending condensation transition.

Bethe ansatz confirms the behavior in the exclusion process.

Abstract

We discuss the long-time limit of the integrated current distribution for the one-dimensional zero-range process with open boundaries. We observe that the current fluctuations become site-dependent above some critical current and argue that this is a precursor of the condensation transition which occurs in such models. Our considerations for the totally asymmetric zero-range process are complemented by a Bethe ansatz treatment for the equivalent exclusion process.