Cancellation phenomenon of barrier escape driven by a non-Gaussian noise

The Lévy noise, with a long-tail distribution induced particle escape from a metastable potential, is shown to display a feature called a cancellation phenomenon, as compared to the Brownian motion case. As a consequence, the escape rate is found to be a nonmonotonous function of the Lévy index mu and the Arrhenius law is not obeyed. We have also derived a rate expression using the reactive flux method, which supports our numerical findings, namely, with the decrease of mu, a large positive flow is allowed to establish at the barrier, however, the probability passing over the saddle point decreases. This implies that the particles outside the barrier come back to the inside and cancel with themselves.