Explosive condensation in a mass transport model

TL;DR

This paper investigates a one-dimensional particle system where increasing local interaction rates lead to rapid formation of a moving condensate, with the relaxation time decreasing logarithmically with system size, indicating instantaneous condensation in large systems.

Contribution

It introduces a new mass transport model exhibiting explosive condensation with a relaxation time decreasing as an inverse power of ln L, contrasting with previous models.

Findings

Clusters accelerate as they gain particles

Condensate moves with increasing speed

Relaxation time scales as inverse power of ln L

Abstract

We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1d lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially spontaneously form in the system, begin to move at increasing speed as they gain particles. Ultimately, they produce a moving condensate which comprises a finite fraction of the mass in the system. We show that, in contrast with previously studied models of condensation, the relaxation time to steady state decreases as an inverse power of ln L with system size L and that condensation is instantenous for L-->infinity.