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Karol Capała¹, Bartłomiej Dybiec¹

¹Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland.

Physical Review. E

|December 17, 2020

Summary

We investigated noise-driven particle motion in bistable potentials, contrasting overdamped and underdamped dynamics. The ratio of transition rates in underdamped systems depends on barrier width and height, unlike overdamped systems.

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Area of Science:

Statistical Physics
Nonlinear Dynamics
Complex Systems

Background:

Noise-driven motion in bistable potentials is a fundamental model in physics.
Understanding escape dynamics is crucial for various physical phenomena.
Existing models often simplify dynamics to overdamped motion.

Purpose of the Study:

To contrast overdamped and full (underdamped) escape dynamics in bistable potentials.
To analyze the influence of potential barrier properties on transition rates.
To develop and validate analytical predictions for underdamped systems.

Main Methods:

Analytical derivations for transition rate ratios.
Numerical simulations of particle dynamics under nonequilibrium, alpha-stable noise.
Comparison of analytical predictions with simulation results.

Main Results:

In the overdamped limit, transition rate ratio depends only on barrier width.
In the full (underdamped) dynamics, the ratio depends on both barrier width and height.
Analytical formulas for underdamped systems are validated by numerical simulations, especially in the weak noise limit.

Conclusions:

Underdamped dynamics introduce a dependence on potential barrier height, absent in overdamped models.
The study provides a more comprehensive understanding of escape dynamics in complex potentials.
Analytical predictions accurately describe escape trajectories characterized by strong noise kicks.