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This study analyzes stochastic systems with power-law trap densities, revealing how medium nonhomogeneity and Lévy flights impact particle dynamics and escape rates, differing significantly from Gaussian processes.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Stochastic systems are fundamental in modeling diverse phenomena.
  • Understanding particle dynamics in heterogeneous media is crucial.
  • Self-similar structures often lead to anomalous diffusion.

Purpose of the Study:

  • To analyze stochastic systems driven by general stable noise.
  • To investigate the influence of position-dependent, power-law trap densities on particle dynamics.
  • To evaluate first passage time distributions and escape rates in one and two dimensions.

Main Methods:

  • Utilizing a random walk description with position-dependent waiting times.
  • Employing the subordination technique for stochastic dynamics with position-dependent time generators.
  • Analyzing one- and two-dimensional systems.

Main Results:

  • Demonstrated the impact of medium nonhomogeneity on first passage time density and escape rate.
  • Evaluated the dependence of escape rate on stability index and memory parameter.
  • Observed significant differences between Gaussian processes and Lévy flights.

Conclusions:

  • The power-law distribution of traps significantly alters particle dynamics.
  • Lévy flights introduce distinct behaviors compared to standard diffusion.
  • The findings offer insights into anomalous transport in complex media.