The Slow Dynamics of the Zero-Range Process in the Framework of the Traps Model

The relaxation dynamics of the zero-range process (ZRP) has been an interesting problem. In this study, we set up the relationship between the ZRP and a model of traps, and investigate the slow dynamics of the ZRP in the framework of the trap 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 resulting 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 the ZRP systems approach the stationary state, the more slowly the particles diffuse.