One-Dimensional Stochastic Lévy-Lorentz Gas

Abstract

We introduce a Lévy-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 $<x^2(t)>\ge C{t}^{3-\gamma }$ for $1<\gamma <2$. This behavior is compatible with a renewal Lévy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.

7 pages, 7 figures (to appear in PRE)

References in corpus (1)

• Superdiffusion and Out-of-equilibrium Chaotic Dynamics with Many Degrees of Freedoms

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