Levy Flights in External Force Fields: From Models to Equations

Details Levy Flights in External Force Fields: From Models to Equations Levy Flights in External Force Fields: From Models to Equations

2002-10-17

arxiv.org/abs/cond-mat/0210387v1

Chemical Physics, 284:409-421 (2002)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 5 figures

Scientific paper

10.1016/S0301-0104(02)00671-7

We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy 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.

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