DYNAMICAL-APPROACH TO ANOMALOUS DIFFUSION - RESPONSE OF LEVY PROCESSES TO A PERTURBATION

Levy statistics are derived from a dynamical system, which can be eith er Hamiltonian or not, using a master equation approach. We compare th ese predictions to the random walk approach recently developed by Zumo fen and Klafter for both the nonstationary [Phys. Rev. E 47, 851 (1993 )] and stationary [Physica A 196, 102 (1993)] case. We study the unper turbed dynamics of the system analytically and numerically and evaluat e the time evolution of the second moment of the probability distribut ion. We also study the response of the dynamical system undergoing ano malous diffusion to an external perturbation and show that if the slow regression to equilibrium of the variable ''velocity'' is triggered b y the perturbation, the process of diffusion of the ''space'' variable takes place under nonstationary conditions and a conductivity steadil y increasing with time is generated in the early part of the response process. In the regime of extremely long times the conductivity become s constant with a value, though, that does not correspond to the presc riptions of the ordinary Green-Kubo treatments.