One-dimensional stochastic Levy-lorentz gas

We introduce a Levy-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 &mgr;(xi) approximately xi(-(1+gamma)). We show that under certain conditions the mean square displacement of the particle obeys <x(2)(t)>>/=Ct3-gamma for 1<gamma<2. This behavior is compatible with a renewal Levy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.