Escape of an inertial Lévy flight particle from a truncated quartic potential well

Motivated by that the quartic potential can confined Lévy flights, we investigate the escape rate of an inertial Lévy particle from a truncated quartic potential well via Langevin simulation. The escape rate still depends on the noise intensity in a power-law form in low noise intensity, but the exponent and the inverse coefficient vary significantly for different Lévy indexes compared with previous works. Trimodal structure of the probability density function was found in simulations. The probability density function in a quasi-stable state exhibits transition among unimodal, bimodal, and trimodal structures. A metastable state by stable state approach is developed to calculate the escape rate analytically, which may be applied to extensive escape problems. The theoretical approach is confirmed by Langevin simulation for the Cauchy case of Lévy flight in the applied potential.