Dynamical continuous time random Lévy flights

Abstract

The Levy flights’ diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Levy random walker in each step flies by obeying the Newton’s Second Law while the nonlinear friction f(v) = − γ0v − γ2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Levy flights converges, behaves localization phenomenon with long time limit, but for the Levy index μ = 2 case, it is still Brownian motion.