Correlated Lévy flight in external force fields

Abstract

The correlated Levy flight is studied analytically in terms of the fractional Fokker-Planck equation and simulated numerically by using the Langevin equation, where the usual white Levy noise is generalized to an Ornstein-Uhlenbeck Levy process (OULP) with a correlation time τc. We analyze firstly the stable behavior of OULP. The probability density function of Levy flight particle driven by the OULP in a harmonic potential is exactly obtained, which is also a Levy-type one with τc-dependence width; when the particle is bounded by a quartic potential, its stationary distribution has a bimodality shape and becomes noticeable with the increase of τc.