Condensation and Clustering in the Driven Pair Exclusion Process

TL;DR

This paper studies how particle condensation and clustering occur in a driven pair exclusion process on lattices, revealing mesoscopic condensates and their spatial correlations influenced by hopping bias.

Contribution

It introduces a model combining pair exclusion with biased hopping, analyzing mesoscopic condensation and clustering phenomena through numerical simulations.

Findings

Condensate size scales as N^β

Number of condensates scales as N^α

Hopping bias induces spatial clustering of condensates

Abstract

We investigate particle condensation in a driven pair exclusion process on one- and two- dimensional lattices under the periodic boundary condition. The model describes a biased hopping of particles subject to a pair exclusion constraint that each particle cannot stay at a same site with its pre-assigned partner. The pair exclusion causes a mesoscopic condensation characterized by the scaling of the condensate size $m_{\rm con}\sim N^\beta$ and the number of condensates $N_{\rm con}\sim N^\alpha$ with the total number of sites $N$. Those condensates are distributed randomly without hopping bias. We find that the hopping bias generates a spatial correlation among condensates so that a cluster of condensates appears. Especially, the cluster has an anisotropic shape in the two-dimensional system. The mesoscopic condensation and the clustering are studied by means of numerical simulations.