Lévy flights with power-law absorption

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.