Steady-State Lévy Flights in a Confined Domain

Details Steady-State Lévy Flights in a Confined Domain Steady-State Lévy Flights in a Confined Domain

2008-04-08

arxiv.org/abs/0804.1301v2

Phys. Rev. E 77, 061112 (2008)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure

Scientific paper

10.1103/PhysRevE.77.061112

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights is derived and solved analytically in the steady state. It is shown that L\'{e}vy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.

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