Barrier crossing of a Lévy flight

• Published in: Europhysics letters Vol. 72; no. 3; pp. 348 - 354
• Main Authors: Chechkin, A. V, Gonchar, V. Yu, Klafter, J, Metzler, R
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.11.2005; EDP Sciences
• Subjects: 02.50.Ey; 05.10.Gg; 05.40.Fb
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/epl/i2005-10265-1

We consider the barrier crossing in a bistable potential for a random-walk process that is driven by Lévy noise of stable index α. 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 μ varies slowly over a large range of the stable index $\alpha\in [1,2)$. For the Cauchy case, we explicitly calculate the escape rate.