Lévy flights in random environments

Abstract

We consider Lévy flights characterized by the step index $f$ in a quenched random force field. By means of a dynamic renormalization group analysis we find that the dynamic exponent $z$ for $f<2$ locks onto $f$, independent of dimension and {\em independent} of the presence of weak quenched disorder. The critical dimension, however, depends on the step index $f$ for $f<2$ and is given by $d_c=2f-2$. For $d<d_c$ the disorder is {\em relevant}, corresponding to a non trivial fixed point for the force correlation function.

12 pages, Latex file, IFA-94/02

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