Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

TL;DR

This paper analyzes an open-boundary zero-range process with temporal correlations, deriving exact steady states, mean-field approximations, and exploring large-deviation properties, revealing a memory-induced phase transition.

Contribution

It introduces an open-boundary zero-range process with temporal correlations and provides exact and approximate solutions, highlighting the impact of memory on current fluctuations.

Findings

Exact steady state for one-site system

Mean-field approximation for larger lattices

Memory-induced dynamical phase transition

Abstract

We study an open-boundary version of the on-off zero-range process introduced in Hirschberg et al. [Phys. Rev. Lett. 103, 090602 (2009)]. This model includes temporal correlations which can promote the condensation of particles, a situation observed in real-world dynamics. We derive the exact solution for the steady state of the one-site system, as well as a mean-field approximation for larger one-dimensional lattices, and also explore the large-deviation properties of the particle current. Analytical and numerical calculations show that, although the particle distribution is well described by an effective Markovian solution, the probability of rare currents differs from the memoryless case. In particular, we find evidence for a memory-induced dynamical phase transition.