Anomalous transport of a tracer on percolating clusters

TL;DR

This paper studies how a tracer moves through a percolating obstacle network, revealing anomalous diffusion, critical scaling, and heterogeneous dynamics near the percolation threshold.

Contribution

It provides a detailed analysis of tracer dynamics on percolating clusters, including scaling laws and response functions at the critical point.

Findings

Mean-square displacement shows anomalous transport at criticality.

Diffusion coefficient exhibits power-law slowing down near the transition.

Dynamic conductivity and non-Gaussian parameter are characterized.

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.