Features of barrier crossing event for Lévy flights
Radiophysics Department, Lobachevsky State University - 23 Gagarin Ave., 603950 Nizhni Novgorod, Russia
Received: 5 December 2015
Accepted: 16 February 2016
The steady-state time characteristics of anomalous diffusion in the form of Lévy flights in a symmetric bistable quartic potential are examined. Based on a previously developed technique, we obtain the exact formula for the correlation time of particle displacement in the case of Cauchy stable noise. The dependence of the correlation time on the height of the potential barrier separating the two stable states and the position of the potential wells is analyzed in detail. As shown, for a sufficiently high potential barrier the correlation time does not depend on its height that can be interpreted as a revision of Kramers' law for Lévy flight superdiffusion.
PACS: 05.40.Fb – Random walks and Levy flights / 02.50.Ga – Markov processes / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EPLA, 2016