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Microscopic dynamics underlying the anomalous diffusion

G. Kaniadakis·G. Lapenta
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Abstract

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.

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BibTeXRIS

G. Kaniadakis, G. Lapenta. 2000-07-19. Microscopic dynamics underlying the anomalous diffusion. https://doi.org/10.1103/physreve.62.3246

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