Barrier crossing driven by Lévy noise: Universality and the role of noise intensity
We study the barrier crossing of a particle driven by white symmetric LÃ©vy noise of index Î± 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, TescâC(Î±)âDÎ¼(Î±), where C(Î±) is a coefficient. It is shown that the exponent Î¼(Î±) remains approximately constant, Î¼â1 for 0<Î±<2; at Î±=2 the power-law form of Tesc changes into the known exponential dependence on 1âD; it exhibits a divergencelike behavior as Î± approaches 2. In this regime we observe a monotonous increase of the escape time Tesc with increasing Î± (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 LÃ©vy steps. For high noise intensities, the escape time curves collapse for all values of Î±. At intermediate noise intensities, the escape time exhibits nonmonotonic dependence on the index Î±, while still retaining the exponential form of the escape time density.