Dynamics of the condensate in zero-range processes

TL;DR

This paper investigates the motion and timescales of the condensate in zero-range processes, revealing that the characteristic time grows polynomially with system size, which is faster than diffusion but not exponential.

Contribution

It provides a detailed analysis of the condensate's ergodic motion and its characteristic timescale in zero-range processes across different geometries.

Findings

Characteristic time grows faster than diffusive timescale

Time scales as a power law of system size in generic cases

Motion behavior is consistent in mean-field and finite-dimensional lattices

Abstract

For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The characteristic time is found to grow with the system size much faster than the diffusive timescale, but not exponentially fast. This holds both in the mean-field geometry and on finite-dimensional lattices. In the generic situation where the critical mass distribution follows a power law, the characteristic time grows as a power of the system size.