Accelerating Brownian motion: A fractional dynamics approach to fast diffusion

¹ School of Chemistry, Tel Aviv University - 69978 Tel Aviv, Israel
² Department of Physics and School of Chemical Sciences University of Illinois at Urbana-Champaign 600 S. Mathews, Urbana, IL61801, USA

Corresponding authors: metzler@post.tau.ac.il klafter@post.tau.ac.il

Received: 5 June 2000
Accepted: 6 July 2000

Abstract

Superdiffusion in the sub-ballistic regime with a non-diverging mean-squared displacement is studied on the basis of a linear, fractional kinetic equation with constant coefficients which is non-local in time and leads to an exponential tail of the corresponding probability density function. It is shown that sub-ballistic superdiffusion can be regarded as ballistic motion with a memory, much as slow diffusion can be thought of as a random walk with a memory. This suggests that fractional kinetic equations are useful in describing both sub- and superdiffusion processes.