Complete Condensation in a Zero Range Process on Scale-Free Networks

Abstract

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.

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• Physical Review Letters - View
• arXiv (Cornell University) - View - PDF
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