A DYNAMICAL-APPROACH TO ANOMALOUS CONDUCTIVITY

We study a process of anomalous diffusion of a variable resulting from the fluctuations of a dichotomous velocity whose two states, in the a bsence of perturbation, have the same waiting time distribution psi(t) . In the long-time limit the function psi(t) is proportional to t(-mu) with 2<mu<3. Previously this distribution along with the constraint o n mu proved to be a dynamical realization of an alpha-stable Levy proc ess with alpha=mu-1. Here we study the response of this anomalous diff usion process to a perturbation which has the effect of truncating the inverse power law of one of the two states of the velocity for times t>1/epsilon, where epsilon is proportional to the intensity of the wea k perturbation. We show that the resulting transport process is charac terized by a succession of two regimes: the first still satisfies the prescriptions of the Green-Kubo approach to conductivity, and, in acco rdance with the nature of the anomalous diffusion studied here, corres ponds to a state of increasing conductivity (IC); the second regime is characterized by a constant conductivity (CC). The transition from th e IC to the CC regime takes place in a time of the order of t similar to 1/epsilon and consequently the transition occurs at longer and long er times, as the perturbation intensity decreases. The final stationar y regime corresponds to an asymmetric Levy process of diffusion.