Condensation phenomena with distinguishable particles

TL;DR

This paper investigates real-space condensation in classical stochastic processes with distinguishable particles, analyzing conditions for condensation and the impact of disorder, especially in the preferential urn model.

Contribution

It analytically clarifies the conditions for condensation in disordered Ehrenfest class processes and explores the role of quenched disorder in the preferential urn model.

Findings

Disorder influences the occurrence of condensation.

Three types of condensation depend on disorder parameters.

Quenched disorder is crucial for condensation phenomena.

Abstract

We study real-space condensation phenomena in a type of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We here study a stochastic process in the Ehrenfest class, i.e., particles in a site are distinguishable. In terms of the statistical mechanical analogue, the Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify conditions for condensation phenomena in disordered cases in the Ehrenfest class. In addition, we discuss the preferential urn model as an example of the disordered urn model. It becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model. It is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters.