Explosive condensation in symmetric mass transport models

TL;DR

This paper investigates how explosive condensation phenomena occur in symmetric mass transport models, revealing that strong non-linearity leads to rapid condensation in one dimension, with higher dimensions likely exhibiting similar behavior.

Contribution

It demonstrates that explosive condensation, previously known for asymmetric models, also occurs in symmetric models under strong non-linearity, supported by heuristic and simulation evidence.

Findings

Explosive condensation occurs in symmetric models with strong non-linearity.

In one dimension, a coarsening regime exists where stationarity time diverges.

Higher dimensions are expected to exhibit explosive condensation for all parameters.

Abstract

We study the dynamics of condensation in a misanthrope process with nonlinear jump rates and factorized stationary states. For large enough density, it is known that such models have a phase separated state, with a non-zero fraction of the total mass concentrating in a single lattice site. It has been established in [B Waclaw and M R Evans, Phys. Rev. Lett., 108(7):070601, 2012] for asymmetric dynamics that such processes exhibit explosive condensation, where the time to reach the stationary state vanishes with increasing system size. This constitutes a spatially extended version of instantaneous gelation which has previously been studied only in mean-field coagulation models. We show that this phenomenon also occurs for symmetric dynamics in one dimension if the non-linearity is strong enough, and we find a coarsening regime where the time to stationarity diverges with the system size for weak non-linearity. In higher space dimensions explosive condensation is expected to be generic for all parameter values. Our results are based on heuristic mean field arguments which are confirmed by simulation data.