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Lévy noise-driven escape from arctangent potential wells.
Karol Capała1, Amin Padash2, Aleksei V Chechkin3
1Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland.
Chaos (Woodbury, N.Y.)
|December 31, 2020
Summary
This study investigates how systems escape potential wells under Lévy noise, specifically Cauchy noise. Findings reveal exponential tails in escape dynamics and analyze potential shape effects on system behavior.
Area of Science:
- Stochastic Dynamical Systems
- Statistical Physics
- Mathematical Modeling
Background:
- Escape from potential wells is fundamental to stochastic dynamical systems.
- Lévy noise models systems with statistical outliers and diverging moments.
- Applications span chemical reactions, ecology, and gene expression.
Purpose of the Study:
- Investigate Lévy noise-driven escape from an arctangent potential well.
- Analyze transient dynamics and analogies to stationary states.
- Examine the influence of potential shape parameters on escape behavior.
Main Methods:
- Utilized Cauchy noise to model Lévy noise-driven escape dynamics.
- Studied an almost rectangular, arctangent potential well with absorbing boundaries.
- Analyzed first-escape time and last-hitting point probability densities.
Main Results:
- Observed analogies between transient dynamics and stationary states of Lévy processes.
- Demonstrated exponential tails in the first-escape dynamics.
- Examined the impact of potential steepness, height, and shape parameters.
Conclusions:
- Lévy noise significantly influences escape dynamics from potential wells.
- Potential well characteristics critically affect escape time and hitting point distributions.
- The study provides insights into systems exhibiting anomalous diffusion and escape phenomena.
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