Stationary and dynamical properties of a zero range process on scale-free networks

Abstract

We study the condensation phenomenon in a zero range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase transition between a condensed phase and an uncondensed phase, and the phase diagram is obtained analytically. As for the dynamical property, we find that the relaxation dynamics depends on the global structure of underlying networks. The relaxation time follows the power law $\tau \sim L^z$ with the network size $L$ in the condensed phase. The dynamic exponent $z$ is found to take a different value depending on whether underlying networks have a tree structure or not.

9 pages, 6 eps figures, accepted version in PRE

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• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation
• Dynamics of condensation in growing complex networks
• Condensation and topological phase transitions in a dynamical network model with rewiring of the links
• Power laws in zero-range processes on random networks
• Balls-in-boxes condensation on networks
• Instability in a Network Coevolving with a Particle System
• Far-from-equilibrium state in a weakly dissipative model
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• Particle Condensation in Pair Exclusion Process
• Structural phase transition in evolving networks
• Condensation phase transition in nonlinear fitness networks
• Zero-range process with long-range interactions at a T-junction
• Tsallis mapping in growing complex networks with fitness
• Finite-size effects in dynamics of zero-range processes
• Slow dynamics of Zero Range Process in the Framework of Traps Model
• Traffic properties for stochastic routings on scale-free networks