Microscopic dynamics underlying the anomalous diffusion
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.
Cite
@article{arxiv.cond-mat/0007311,
title = {Microscopic dynamics underlying the anomalous diffusion},
author = {G. Kaniadakis and G. Lapenta},
journal= {arXiv preprint arXiv:cond-mat/0007311},
year = {2009}
}
Comments
4 pag. - no figures. To appear on Phys. Rev. E 62, September 2000