Condensation in zero-range processes on inhomogeneous networks

TL;DR

This paper studies how inhomogeneities in networks influence condensation in zero-range processes, revealing that degree ratios trigger condensation and affect condensate stability and melting times.

Contribution

It introduces a model linking network degree inhomogeneity to condensation dynamics, highlighting the impact of degree ratios on condensate formation and stability.

Findings

Condensation is triggered by the ratio of highest to average degree.

The condensate occupation can oscillate widely.

Melting time of the condensate grows exponentially with system size.

Abstract

We investigate the role of inhomogeneities in zero-range processes in condensation dynamics.We consider the dynamics of balls hopping between nodes of a network, and find that the condensation is triggered by the ratio k_1/k of the highest degree k_1 to the average degree k. Although the condensate takes on the average an extensive number of balls, its occupation can oscillate in a wide range. We show that in systems with strong inhomogeneity, the typical melting time of the condensate grows exponentially with the number of balls.