Escape rate of Lévy particles from truncated confined and unconfined potentials

For a double-well potential consisting of a truncated quartic potential and a truncated harmonic potential, the inter-well escape rates of Lévy particles are investigated numerically, and analytically for the Cauchy case, with focus on the former. The escape rate of Lévy particles from the truncated confined quartic potential well possesses qualitatively different characteristics compared with that from the truncated harmonic potential well, as reflected in the noise intensity dependence and Lévy index dependence of the escape rate. Two kinds of different escape mechanisms exist for low noise and high noise intensities. As the noise intensity increases, the escaping particles in quasi-stationary state present a noise-induced phase transition phenomenon, wherein the distribution of Lévy particles transits from a bimodal narrow distribution to a unimodal wide distribution. The characteristics of the escape rate in low and high noise intensities can be understood by the distributions of Lévy particles and the features of Lévy noise.