Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions

Details Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions

1998-10-15

arxiv.org/abs/cond-mat/9810176v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, Revtex file, 6 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.59.2736

We consider Levy flights subject to external force fields. This anomalous transport process is described by two approaches, a Langevin equation with Levy noise and the corresponding generalized Fokker-Planck equation containing a fractional derivative in space. The cases of free flights, constant force and linear Hookean force are analyzed in detail, and we corroborate our findings with results from numerical simulations. We discuss the non-Gibbsian character of the stationary solution for the case of the Hookean force, i.e. the deviation from Boltzmann equilibrium for long times. The possible connection to Tsallis's q-statistics is studied.

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