Continuously varying exponents in the distribution of waiting times in the symmetric exclusion process on a percolation cluster

Abstract

We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backbone. We show that the probability that a tagged particle occupies the same position at time $t_0+t$ as at time $t_0$ decays algebraically as $t^{-\omega}$, where the exponent $\omega$ varies continuously with particle density for densities above a threshold value $\rho^*<1$. We also investigate the correlations between successive waiting times along the trajectory of a tagged particle.