Spectral characteristics of steady-state Lévy flights in confinement potential profiles

Abstract

The steady-state correlation characteristics of superdiffusion in the form of Lévy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type . For these potential profiles and arbitrary Lévy index α, we obtain the asymptotic expression of the spectral power density.