Particle Condensation in Pair Exclusion Process

TL;DR

This paper investigates how weak pair exclusion interactions alter condensation phenomena, leading to multiple mesoscopic condensates with specific scaling behaviors, demonstrated through analytical mapping and numerical confirmation.

Contribution

It introduces a modified zero-range process with pair exclusion, revealing a new condensation regime with multiple mesoscopic condensates and their scaling laws.

Findings

Multiple mesoscopic condensates scale as N^{1/2}

Number of condensates scales as N^{1/2} with logarithmic correction

Analytical results confirmed by numerical simulations

Abstract

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size $N$. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the zero-range process by including a pair exclusion. Each particle is associated with its own partner, and particles of a pair are forbidden to stay at the same site. The pair exclusion is weak in that a particle interacts with only a single one among all others. It turns out that such a weak interaction changes the nature of condensation drastically. There appear a number of mesoscopic condensates: the mass of a condensate scales as $m_{\rm con}\sim N^{1/2}$ and the number of condensates scales as $N_{\rm con} \sim N^{1/2}$ with a logarithmic correction. These results are derived analytically through a mapping to a solvable model under a certain assumption, and confirmed numerically.