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

Area of Science:

• Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Lévy walk is a physical model for superdiffusion with finite velocity.
• Particle movement is often influenced by external potentials.
• Understanding particle behavior in force fields is crucial.

Purpose of the Study:

• To establish a Langevin system coupled with a subordinator for Lévy walk in time-dependent periodic force fields.
• To analyze the effects of external forces on particle dynamics.
• To derive the generalized Klein-Kramers equation for time- and space-dependent forces.

Main Methods:

• Coupling a Langevin system with a subordinator.
• Analyzing particle movement under time-dependent periodic forces.
• Deriving the generalized Klein-Kramers equation.

Main Results:

• External forces cause a nonzero first moment despite periodicity.
• Additional dispersion in particle position is observed.
• Ensemble- and time-averaged mean-squared displacements are consistently influenced.
• Generalized Klein-Kramers equation derived for time- and space-dependent forces.

Conclusions:

• The established model accurately describes Lévy walk in complex force fields.
• External forces significantly alter superdiffusive particle behavior.
• The derived Klein-Kramers equation provides a framework for further analysis.