Inertial Lévy Flight with Nonlinear Friction

Lévy flight with nonlinear friction is studied. Due to the occurrence of extremely long jumps Lévy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass. However, by introducing nonlinear friction, we show that the stochastic process subject to Lévy noise exhibits finite variance, leading to a well-defined kinetic energy. In the force-free field, normal diffusion behavior is observed and the diffusion coefficient decreases with Lévy index μ. Furthermore, we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γ₀ determines whether resonance occurs or not.