Anomalous transport of a tracer on percolating clusters

Abstract

We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.