Balls-in-boxes condensation on networks

TL;DR

This paper investigates how condensates form in zero-range processes on different network types, revealing distinct static and dynamic behaviors depending on network regularity and symmetry breaking.

Contribution

It introduces a minimal irregularity model on networks, analyzing how symmetry breaking influences condensate formation and melting times in zero-range processes.

Findings

Condensate formation differs between regular and irregular networks.

Melting time scales exponentially with system size on irregular networks.

Spontaneous symmetry breaking leads to power-law melting times on regular networks.

Abstract

We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q-node with degree Q>q. The statics and dynamics of the condensation depends on the parameter log(Q/q), which controls the exponential fall-off of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q-node which increases exponentially with the system size $N$. This behavior is different than that on a q-regular network where log(Q/q)=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q-nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.