Lévy-walk-like Langevin dynamics affected by a time-dependent force

Abstract

Lévy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In this paper, we establish a Langevin system coupled with a subordinator to describe the Lévy walk in the time-dependent periodic force field. The effects of external force are detected and carefully analyzed, including nonzero first moment (even though the force is periodic), adding an additional dispersion on the particle position, the consistent influence on the ensemble- and time-averaged mean-squared displacement, etc. Besides, the generalized Klein-Kramers equation is obtained, not only for the time-dependent force but also for space-dependent one.

13 pages, 2 figures

References in corpus (7)

• Lévy walks
• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Space-time velocity correlation function for random walks
• Subdiffusion in an external force field
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Lévy walk dynamics in an external harmonic potential
• Langevin picture of Lévy walk in a constant force field