Maintenance of order in a moving strong condensate

TL;DR

This paper studies a minimal driven mass transport model revealing a moving strong condensate phase that appears under certain conditions, characterized by a condensate moving through the system and replenished by low occupancy sites.

Contribution

It introduces a new model with a specific hopping rate and demonstrates the existence of a moving strong condensate phase, including analytical estimates and numerical validation.

Findings

A moving strong condensate phase exists for certain parameters.

The transition to this phase is of mixed order with a discontinuity and diverging length scale.

Numerical results confirm the analytical estimates for the critical parameters.

Abstract

We investigate the conditions under which a moving condensate may exist in a driven mass transport system. Our paradigm is a minimal mass transport model in which $n-1$ particles move simultaneously from a site containing $n>1$ particles to the neighbouring site in a preferred direction. In the spirit of a Zero-Range process the rate $u(n)$ of this move depends only on the occupation of the departure site. We study a hopping rate $u(n) = 1 + b/n^\alpha$ numerically and find a moving strong condensate phase for $b > b_c(\alpha)$ for all $\alpha >0$. This phase is characterised by a condensate that moves through the system and comprises a fraction of the system's mass that tends to unity. The mass lost by the condensate as it moves is constantly replenished from the trailing tail of low occupancy sites that collectively comprise a vanishing fraction of the mass. We formulate an approximate analytical treatment of the model that allows a reasonable estimate of $b_c(\alpha)$ to be obtained. We show numerically (for $\alpha=1$) that the transition is of mixed order, exhibiting exhibiting a discontinuity in the order parameter as well as a diverging length scale as $b\searrow b_c$.