Condensation in Temporally Correlated Zero-Range Dynamics

TL;DR

This paper investigates how temporal correlations in non-Markovian zero-range processes influence condensation, revealing that memory effects can alter steady states and cause the condensate to drift in one-dimensional systems.

Contribution

It introduces and analyzes a non-Markovian zero-range process, showing how memory effects modify condensation behavior and lead to condensate drift.

Findings

Mean-field steady state resembles Markovian ZRP with modified rates

Condensate occupies two sites and drifts in 1D systems

Memory effects significantly impact condensation scenarios

Abstract

Condensation phenomena in non-equilibrium systems have been modeled by the zero-range process, which is a model of particles hopping between boxes with Markovian dynamics. In many cases, memory effects in the dynamics cannot be neglected. In an attempt to understand the possible impact of temporal correlations on the condensate, we introduce and study a process with non-Markovian zero-range dynamics. We find that memory effects have significant impact on the condensation scenario. Specifically, two main results are found: (1) In mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation, and (2) for nearest-neighbor hopping in one dimension, the condensate occupies two adjacent sites on the lattice and drifts with a finite velocity. The validity of these results in a more general context is discussed.