LEVY FLIGHTS WITH QUENCHED NOISE AMPLITUDES

We study the one-dimensional random walk of a particle in the presence of a short-range correlated quenched random field of jump lengths I(x ) drawn from a Levy type distribution p(l) similar to l(-1-f) with 0 < f < 2. We find the stochastic dynamics to be characterized by a novel length-time scaling relation that is caused by an effective jump-leng th distribution p(eff)(l) similar to l(-l-g) in the stationary state, which decays more rapidly than p(l), i.e. g greater than or equal to f . For f greater than or similar to 1.3, g becomes larger than 2 and th e particle diffuses normally although p(l) has no finite second moment . A scaling theory is developed that describes the dynamical crossover from the annealed to the quenched situation.