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 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