Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model
Statistical Mechanics
2015-06-24 v1
Abstract
We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.
Cite
@article{arxiv.cond-mat/0107497,
title = {Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model},
author = {Ralf Metzler and Igor M. Sokolov},
journal= {arXiv preprint arXiv:cond-mat/0107497},
year = {2015}
}
Comments
4 pages, REVTeX