Barrier crossing of a Lévy flightA. V. Chechkin1, V. Yu. Gonchar1, J. Klafter2 and R. Metzler3
1 Institute for Theoretical Physics NSC KIPT - Akademicheskaya st. 1 61108 Kharkov, Ukraine
2 School of Chemistry, Tel Aviv University - 69978 Tel Aviv, Israel
3 NORDITA (Nordic Institute for Theoretical Physics) - Blegdamsvej 17 2100 Copenhagen Ø, Denmark
received 17 May 2005; accepted in final form 16 September 2005
published online 12 October 2005
We consider the barrier crossing in a bistable potential for a random-walk process that is driven by Lévy noise of stable index . It is shown that the survival probability decays exponentially, but with a power law dependence of the mean escape time on the noise intensity D. Here C is a constant, and the exponent varies slowly over a large range of the stable index . For the Cauchy case, we explicitly calculate the escape rate.
05.40.Fb - Random walks and Levy flights.
02.50.Ey - Stochastic processes.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
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