## 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.(c) 2007 American Institute of Physics.

Original language | English |
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Article number | 026112 |

Pages (from-to) | - |

Number of pages | 6 |

Journal | Chaos |

Volume | 17 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2007 |

## Keywords

- THERMODYNAMICS
- TRANSITION
- MODEL