Dynamics of condensation in zero-range processes

TL;DR

This paper investigates the time evolution and scaling behavior of condensation in zero-range processes, revealing how dimensionality and bias influence the dynamical exponents associated with condensate growth.

Contribution

It provides a detailed analytical and numerical study of the dynamics of condensation in zero-range processes, highlighting differences between mean-field and one-dimensional systems, and the effects of bias.

Findings

The dynamical exponent z changes from 2 (mean-field) to 3 in one dimension.

The critical fluctuation exponent z_c increases from 2 to approximately 5 in one dimension.

Bias restores the mean-field dynamical exponent z=2 and reduces z_c to about 3.

Abstract

The dynamics of a class of zero-range processes exhibiting a condensation transition in the stationary state is studied. The system evolves in time starting from a random disordered initial condition. The analytical study of the large-time behaviour of the system in its mean-field geometry provides a guide for the numerical study of the one-dimensional version of the model. Most qualitative features of the mean-field case are still present in the one-dimensional system, both in the condensed phase and at criticality. In particular the scaling analysis, valid for the mean-field system at large time and for large values of the site occupancy, still holds in one dimension. The dynamical exponent $z$, characteristic of the growth of the condensate, is changed from its mean-field value 2 to 3. In presence of a bias, the mean-field value $z=2$ is recovered. The dynamical exponent $z_c$, characteristic of the growth of critical fluctuations, is changed from its mean-field value 2 to a larger value, $z_c\simeq 5$. In presence of a bias, $z_c\simeq 3$.