title: Balls-in-boxes condensation on 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 depend on the parameter alpha=ln Q/q, which controls the exponential falloff 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 alpha=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.
authors.affiliation: Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Kraków, Poland. bogacz@th.if.uj.edu.pl
authors.forename: L
authors.initials: L
authors.lastname: Bogacz
authors.forename: Z
authors.initials: Z
authors.lastname: Burda
authors.forename: W
authors.initials: W
authors.lastname: Janke
authors.forename: B
authors.initials: B
authors.lastname: Waclaw