Chaos-induced escape over a potential barrier

Area of Science:

• Statistical physics
• Nonlinear dynamics
• Chemical kinetics

Background:

• Particle escape from potential wells is a fundamental process in many physical and chemical systems.
• The Kramers escape rate theory typically assumes symmetric noise fluctuations.
• Chaotic dynamics can introduce complex, asymmetric noise patterns.

Purpose of the Study:

• To investigate the impact of statistically asymmetric, chaos-generated noise on particle escape rates.
• To determine how noise asymmetry influences particle distribution within a potential well.
• To develop an analytical framework for understanding these effects.

Main Methods:

• Analysis of chaos-generated noise properties.
• Investigation of particle dynamics in a potential well under asymmetric noise.
• Application of the Perron-Frobenius equation for analytical solutions.
• Perturbative analysis to approximate escape rates.

Main Results:

• Statistical asymmetry in chaotic noise leads to a skewed Maxwell-Boltzmann distribution.
• The Kramers escape rate is either enhanced or suppressed depending on the direction of the skew.
• An analytical expression for the escape rate's prefactor, accounting for asymmetry, was derived.
• In the zeroth-order limit, particle escape rate converges to the standard Kramers rate.

Conclusions:

• Chaotic noise asymmetry is a critical factor influencing particle escape dynamics.
• The derived analytical expression provides a quantitative tool for predicting escape rates under asymmetric conditions.
• Understanding these effects is crucial for systems involving noise-driven transitions.