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Lévy flights with power-law absorption.

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Area of Science:

  • Statistical physics
  • Stochastic processes
  • Condensed matter physics

Background:

  • Stochastic particle motion is fundamental in various physical phenomena.
  • Understanding target-trapping dynamics is crucial for processes like diffusion and reaction kinetics.

Purpose of the Study:

  • To investigate the trapping probability of a particle undergoing power-law distributed stochastic motion in a 1D lattice.
  • To analyze the influence of target distribution on the trapping dynamics.

Main Methods:

  • Analytical derivation of trapping probability.
  • Numerical simulations of particle trajectories.
  • Analysis of power-law distributions for jump lengths and target locations.

Main Results:

  • A finite probability of never being trapped exists if the jump length exponent (μ) is less than the target distribution exponent (α).
  • Power-law target distributions significantly impact trapping dynamics.
  • Simulations confirm analytical findings and reveal slow searching times in finite systems.

Conclusions:

  • The interplay between particle motion and target distribution determines the ultimate trapping of a stochastic walker.
  • The study provides insights into conditions where a particle might evade capture indefinitely in a 1D system.
  • Findings have implications for understanding diffusion-limited reactions and search processes in complex environments.