Features of barrier crossing event for Lévy flights

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.