Anomalous diffusion on percolating clusters

Yuval Gefen; Amnon Aharony; Shlomo Alexander

doi:10.1103/PhysRevLett.50.77

Anomalous diffusion on percolating clusters

Yuval Gefen, Amnon Aharony, Shlomo Alexander

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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.

Original language	English
Pages (from-to)	77-80
Number of pages	4
Journal	Physical Review Letters
Volume	50
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevLett.50.77
State	Published - 1 Jan 1983
Externally published	Yes

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Physics and Astronomy (all)

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10.1103/PhysRevLett.50.77

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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.",

author = "Yuval Gefen and Amnon Aharony and Shlomo Alexander",

note = "Funding Information: The author is grateful to the Slovak Grant Agency for 11990177f)o r partial supportingo f this work.",

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AB - 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.

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Anomalous diffusion on percolating clusters

Abstract

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