Lévy flights in random environments.

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 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 dc = 2f − 2. For d < dc the disorder is relevant, corresponding to a non trivial fixed point for the force correlation function. PACS No. 1993: 02.50.Ey, 02.50.Ga, 05.20.-y, 05.40.+j, 05.60.+w, 05.70.Ln, 44.30.+v, 47.55.-t [†] E-mail: [email protected]