One-Dimensional Stochastic Lévy-Lorentz Gas

Details One-Dimensional Stochastic Lévy-Lorentz Gas One-Dimensional Stochastic Lévy-Lorentz Gas

2000-02-06

arxiv.org/abs/cond-mat/0002084v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 7 figures (to appear in PRE)

Scientific paper

10.1103/PhysRevE.61.1164

We introduce a L\'evy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers $\{\xi_i \}$ are independent random variables identically distributed according to the probability density function $\mu(\xi )\sim \xi^{-(1 + \gamma)}$. We show that under certain conditions the mean square displacement of the particle obeys $ \ge C t^{3 - \gamma}$ for $1 < \gamma < 2$. This behavior is compatible with a renewal L\'evy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.

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