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

TL;DR

This paper analyzes how zero range processes on scale-free networks exhibit phase transitions and how their relaxation dynamics depend on network structure, revealing different dynamic exponents for tree and non-tree networks.

Contribution

It provides an analytical phase diagram for condensation in zero range processes on scale-free networks and uncovers how network topology influences relaxation times.

Findings

Stationary state depends only on degree distribution.

Phase transition between condensed and uncondensed states.

Relaxation time scales as τ ~ L^z with network size.

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.