Coarsening, condensates and extremes in aggregation-fragmentation models

TL;DR

This paper investigates the coarsening dynamics and condensate formation in aggregation-fragmentation models using extreme value statistics, revealing anomalously large fluctuations and a pre-asymptotic state during coarsening.

Contribution

It introduces a novel application of extreme value statistics to analyze coarsening in aggregation models, highlighting the role of pre-asymptotic states and fluctuation behavior.

Findings

Condensates form on a growing coarsening length scale.

Local condensate mass distribution exhibits scaling and large fluctuations.

System dynamics during coarsening are governed by a pre-asymptotic state.

Abstract

We use extreme value statistics to study the dynamics of coarsening in aggregation-fragmentation models which form condensates in the steady state. The dynamics is dominated by the formation of local condensates on a coarsening length scale which grows in time in both the zero range process and conserved mass aggregation model. The local condensate mass distribution exhibits scaling, which implies anomalously large fluctuations, with mean and standard deviation both proportional to the coarsening length. Remarkably, the state of the system during coarsening is governed not by the steady state, but rather a pre-asymptotic state in which the condensate mass fluctuates strongly.