Microscopic dynamics underlying the anomalous diffusion

Details Microscopic dynamics underlying the anomalous diffusion Microscopic dynamics underlying the anomalous diffusion

2000-07-19

arxiv.org/abs/cond-mat/0007311v1

Phys.Rev.E 62, 3246 (2000).

Physics

Condensed Matter

Statistical Mechanics

4 pag. - no figures. To appear on Phys. Rev. E 62, September 2000

Scientific paper

10.1103/PhysRevE.62.3246

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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