Slow dynamics of Zero Range Process in the Framework of Traps Model

TL;DR

This paper explores the slow relaxation dynamics of the zero range process (ZRP) by linking it to the traps model, revealing how particle interactions and condensation influence aging and diffusion behaviors.

Contribution

It establishes an analytical relationship between ZRP and traps model, analyzing how particle interactions affect slow dynamics and aging in ZRP systems.

Findings

Particle interactions cause significant effects on dynamics.

Condensation influences relaxation and escape times.

Diffusion slows as ZRP approaches stationary state.

Abstract

The relaxation dynamics of zero range process (ZRP) has always been an interesting problem. In this study, we set up the relationship between ZRP and traps model, and investigate the slow dynamics of ZRP in the framework of traps model. Through statistical quantities such as the average rest time, the particle distribution, the two-time correlation function and the average escape time, we find that the particle interaction, especially the resulted condensation, can significantly influence the dynamics. In the stationary state, both the average rest time and the average escape time caused by the attraction among particles are obtained analytically. In the transient state, a hierarchical nature of the aging dynamics is revealed by both simulations and scaling analysis. Moreover, by comparing the particle diffusion in both the transient state and the stationary state, we find that the closer ZRP systems approach the stationary state, the more slowly particles diffuse.