Summary: Leevy flights in external force fields: from models to equations
, I.M. Sokolovb,*
Max-Planck-Institut fuur Stroomungsforschung, Goottingen, Germany
Institut fuur Physik, Humboldt-Universitaat zu Berlin, Invalidenstraße 110, D-10115 Berlin, Germany
Received 13 December 2001
We consider different generalizations of the FokkerPlanck equation (FPE) devised to describe Leevy processes in
potential force fields. We show that such generalizations can proceed along different lines. On one hand, Leevy statistics
can emerge from the fractal temporal nature of the underlying process, i.e., a high variability in the rate of microscopic
events. On the other hand, they may be a direct consequence of the scale-free spatial structure on which the process
evolves. Although both forms considered lead to Boltzmann equilibrium, the relaxation patterns are quite different. As
an example, generalized diffusion in a double-well potential is considered.
Ó 2002 Elsevier Science B.V. All rights reserved.
Random walk processes leading to anomalous
diffusion are adequate for describing various
physical situations. The continuous time random