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One-Dimensional Stochastic Lévy-Lorentz Gas

E. Barkai·V. Fleurov·J. Klafter
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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 $\{ξ_i \}$ are independent random variables identically distributed according to the probability density function $μ(ξ)\sim ξ^{-(1 + γ)}$. We show that under certain conditions the mean square displacement of the particle obeys $ \ge C t^{3 - γ}$ for $1 < γ< 2$. 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.

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BibTeXRIS

E. Barkai, V. Fleurov, J. Klafter. 2000-02-06. One-Dimensional Stochastic Lévy-Lorentz Gas. https://doi.org/10.1103/physreve.61.1164

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