Condensation transition in zero-range processes with diffusion

TL;DR

This paper investigates a one-dimensional urn model with particle hopping and diffusion, analyzing the conditions for condensation transition and mapping the dynamics to driven-diffusive systems, using mean field and numerical methods.

Contribution

It introduces a new urn model with diffusion, studies its phase diagram for condensation, and connects it to driven-diffusive systems.

Findings

Condensation transition depends on parameters b and alpha.

Phase diagram mapped within mean field approximation.

Numerical simulations support theoretical predictions.

Abstract

Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an urn to its nearest neighbor by a rate which decays with the occupation number k of the departure site as (1+b/k). In addition a diffusion process takes place, whereby all particles in an urn may hop to an adjacent one with some rate alpha$. Condensation transition which may take place in this model is studied and the (b,alpha) phase diagram is calculated within the mean field approximation and by numerical simulations. A driven-diffusive model whose coarse grained dynamics corresponds to this urn model is considered.