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 particle jumping rate function $p(n)=n^{\delta }$. We show analytically that a complete condensation occurs when $\delta \le {\delta }_c\equiv 1/(\gamma -1)$ 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 $\tau \sim L^z$ with the network size $L$ and a dynamic exponent $z$ in the condensed phase.

4 pages, 2 EPS figures, and 1 table (some revision for relational dynamics parts)

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