Coarsening dynamics in condensing zero-range processes and size-biased birth death chains

TL;DR

This paper studies the coarsening dynamics in zero-range processes with decreasing jump rates, introducing a size-biased birth-death chain to analyze the condensation transition and mass transport behavior.

Contribution

It extends previous models by developing a size-biased process to better understand the condensed phase dynamics, providing a novel analytical tool.

Findings

Derived effective single-site dynamics for coarsening behavior.

Introduced a size-biased birth-death chain as a new analytical tool.

Results supported by heuristic analysis and simulations.

Abstract

Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in [C. Godreche, J. Phys. A: Math. Gen., 36(23) 6313 (2003)] to derive effective single site dynamics which form a non-linear birth death chain describing the coarsening behaviour. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.