Lévy-walk-like Langevin dynamics with random parameters.

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Anomalous diffusion is prevalent in complex, inhomogeneous environments.
• Lévy walks are a model for anomalous diffusion, exhibiting superdiffusion.

Purpose of the Study:

• To characterize particle trajectories in inhomogeneous environments using an underdamped Langevin system coupled with a subordinator.
• To investigate the influence of random system parameters (relaxation timescale τ, velocity diffusivity σ) on Lévy walk dynamics.

Main Methods:

• Modeling particle motion via an underdamped Langevin system.
• Coupling the Langevin system with a subordinator to represent anomalous diffusion.
• Analyzing the effects of random τ and σ on diffusion behavior.

Main Results:

• Random velocity diffusivity (σ) has a trivial effect on the ensemble-averaged diffusion.
• A specific distribution of random relaxation timescale (τ) slows the velocity correlation decay.
• Random τ competes with the inherent superdiffusion of the Lévy walk and depends on the subordinator.

Conclusions:

• Random system parameters introduce novel dynamics in anomalous diffusion, requiring detailed analysis.
• The distribution of relaxation time (τ) significantly impacts diffusion behavior in complex systems.
• Understanding these parameters is crucial for accurately modeling anomalous diffusion.