The Nature of the Condensate in Mass Transport Models

TL;DR

This paper investigates the conditions and characteristics of real space condensation in one-dimensional mass transport models, identifying two regimes with distinct condensate shapes and fluctuation behaviors.

Contribution

It derives the criterion for condensation and analyzes the shape and size of the condensate, revealing two distinct fluctuation regimes and their interpretations.

Findings

Two regimes of condensate behavior identified

Gaussian and non-Gaussian condensate distributions characterized

Fluctuation scaling laws established for each regime

Abstract

We study the phenomenon of real space condensation in the steady state of a class of one dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and analyse the precise nature of the shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as $L^{1/2}$ where $L$ is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. We interpret these results within the framework of sums of random variables.