ANOMALOUS DIFFUSION IN DISORDERED MEDIA - STATISTICAL MECHANISMS, MODELS AND PHYSICAL APPLICATIONS

The subject of this paper is the evolution of Brownian particles in disordered environments. The "Ariadne's clew" we follow is understanding of the general statistical mechanisms which may generate "anomalous" (non-Brownian) diffusion laws; this allows us to develop simple arguments to obtain a qualitative (but often quite accurate) picture of most situations. Several analytical techniques-such as the Green function formalism and renormalization group methods-are also exposed. Care is devoted to the problem of sample to sample fluctuations, particularly acute here. We consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder. An effort is made to illustrate the theoretical models by describing many physical situations where anomalous diffusion laws have been-or could be-observed. © 1990.