Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site

TL;DR

This paper investigates how condensation transitions occur in a one-dimensional zero-range process with a defect site, revealing two mechanisms and explaining finite-size effects on particle current.

Contribution

It identifies two distinct condensation mechanisms in the grand canonical ensemble and explains finite-size effects on particle current in the canonical ensemble.

Findings

Two condensation mechanisms in grand canonical ensemble

Discrepancies in current-density diagrams for finite systems

Finite current exceeds maximum predicted for infinite systems

Abstract

Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' particle current versus particle density diagrams are investigated and an explanation for how the finite current goes above a maximum value predicted for infinite systems is found in the canonical ensemble.