Europhys. Lett.
Volume 72, Number 3, November 2005
Page(s) 348 - 354
Section General
Published online 12 October 2005
Europhys. Lett., 72 (3), pp. 348-354 (2005)
DOI: 10.1209/epl/i2005-10265-1

Barrier crossing of a Lévy flight

A. 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 $\alpha$. It is shown that the survival probability decays exponentially, but with a power law dependence $T_c(\alpha,D)=C(\alpha)D^{-\mu (\alpha)}$ of the mean escape time on the noise intensity D. Here C is a constant, and the exponent $\mu$ varies slowly over a large range of the stable index $\alpha\in
[1,2)$. 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.).

© EDP Sciences 2005