Escape process in systems characterized by stable noises and position-dependent resting times

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.