Anomalous Diffusion on Percolating Clusters

Yuval Gefen, Amnon Aharony, and Shlomo Alexander
Phys. Rev. Lett. 50, 77 – Published 3 January 1983
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Abstract

The mean square distance reached after t random-walk steps on a percolating cluster is shown to behave as t2(2+θ) (instead of t) for short times (for which the cluster is seen to be self-similar). The exponent θ is related to that describing the dc conductivity near percolation. Averaging over all clusters yields the ac conductivity and dielectric constant near percolation in the high-frequency limit, when the polarization of the medium is unimportant.

  • Received 7 September 1982

DOI:https://doi.org/10.1103/PhysRevLett.50.77

©1983 American Physical Society

Authors & Affiliations

Yuval Gefen and Amnon Aharony

  • Department of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Israel

Shlomo Alexander

  • The Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

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Issue

Vol. 50, Iss. 1 — 3 January 1983

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