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Journal Articles Journal de Physique Year : 1987

Anomalous diffusion in random media of any dimensionality

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Abstract

We show, through physical arguments and a renormalization group analysis, that in the presence of long-range correlated random forces, diffusions is anomalous in any dimension. We obtain in general surdiffusive behaviours, except when the random force is the gradient of a potential. In this last situation, with either short or long-range correlations, a subdiffusive behaviour with a disorder dependent exponent is found in the upper critical case (D = 2 for short-range correlations). This is because the β-function vanishes, which is explicitly proven at all orders of the perturbation theory. Apart from this case, a potential force is expected to lead to logarithmic diffusion (1/f noise), as suggested by simple arguments.
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Dates and versions

jpa-00210574 , version 1 (01-01-1987)

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J.P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal. Anomalous diffusion in random media of any dimensionality. Journal de Physique, 1987, 48 (9), pp.1445-1450. ⟨10.1051/jphys:019870048090144500⟩. ⟨jpa-00210574⟩
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