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arXiv · 1012.0470

Anomalous transport of a tracer on percolating clusters

Markus Spanner·Felix Höfling·Gerd Schröder-Turk·Klaus Mecke·Thomas Franosch
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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.

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Markus Spanner, Felix Höfling, Gerd Schröder-Turk, Klaus Mecke, Thomas Franosch. 2010-12-02. Anomalous transport of a tracer on percolating clusters. https://doi.org/10.1088/0953-8984%2F23%2F23%2F234120

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