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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.