NON-BROWNIAN TRANSPORT IN COMPLEX-SYSTEMS

In this paper we review some approaches that lead to deviations from t he well known Brownian motion. We focus on the less explored enhanced diffusion for which the mean-squared displacement is superlinear in ti me. Such a behavior appears to be generic in various nonlinear Hamilto nian systems. We discuss the Levy walk scheme that gives rise to such enhancement and calculate the corresponding propagators. An applicatio n to a family of one-dimensional maps is presented.