Escape by jumps and diffusion by 𝛼-stable noise across the barrier in a double well potential

Inspired by the previous evidence that the DO events can be modelled as transitions driven by Lévy noise, we perform a detailed numerical study of the average transition rate in a double well potential for a Langevin equation driven by Lévy noise. The potential considered has the height and width of the potential barrier as free parameters, which allows to study their influence separately. The results show that there are two different behaviours depending on the noise intensity. For high noise intensity the transitions are dominated by gaussian diffusion and follow Kramer’s law. When noise intensity decreases the average transition time changes to the expected power law only dependent on the width on the potential and not on the height. Moreover, we find a scaling under which the transition time collapses for all heights and widths into a universal curve, only dependent on 𝛼.