Barrier crossing driven by Lévy noise: Universality and the role of noise intensity

Abstract

We study the barrier crossing of a particle driven by white symmetric Lévy noise of index alpha and intensity D for three different generic types of potentials: (a) a bistable potential, (b) a metastable potential, and (c) a truncated harmonic potential. For the low noise intensity regime we recover the previously proposed algebraic dependence on D of the characteristic escape time, T_{esc} approximately C(alpha)D;{mu(alpha)} , where C(alpha) is a coefficient. It is shown that the exponent mu(alpha) remains approximately constant, mu approximately 1 for 0<alpha<2 ; at alpha=2 the power-law form of T_{esc} changes into the known exponential dependence on 1D ; it exhibits a divergencelike behavior as alpha approaches 2. In this regime we observe a monotonous increase of the escape time T_{esc} with increasing alpha (keeping the noise intensity D constant). The probability density of the escape time decays exponentially. In addition, for low noise intensities the escape times correspond to barrier crossing by multiple Lévy steps. For high noise intensities, the escape time curves collapse for all values of alpha . At intermediate noise intensities, the escape time exhibits nonmonotonic dependence on the index alpha , while still retaining the exponential form of the escape time density.