Noise-induced phase space transport in two-dimensional Hamiltonian systems

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Chaotic orbits in Hamiltonian systems can exhibit long-term confinement near regular islands, a phenomenon known as
• stickiness
• .
• Understanding the mechanisms that destabilize these sticky orbits is crucial for predicting system behavior under external influences.

Purpose of the Study:

• To investigate how low-amplitude perturbations, specifically noise and periodic driving, accelerate phase space diffusion.
• To quantify the relationship between perturbation amplitude and the escape time of sticky chaotic orbits.
• To compare the efficacy of different types of noise and periodic driving in destabilizing these orbits.

Main Methods:

• First passage time experiments were employed to analyze the dynamics of two-dimensional Hamiltonian systems.
• Simulations were conducted using both additive and multiplicative white noise, as well as colored noise.
• The effects of periodic driving at various frequencies were systematically studied.

Main Results:

• Both noise and periodic driving significantly reduce the escape time of sticky chaotic orbits, with escape time scaling logarithmically with perturbation amplitude.
• For white noise, the type of noise (additive/multiplicative) and the presence of friction are largely irrelevant.
• Colored noise and periodic driving are most effective when their frequencies match the natural frequencies of the unperturbed orbits, indicating a resonance phenomenon.

Conclusions:

• Low-amplitude perturbations can act as a powerful mechanism for accelerating phase space diffusion in Hamiltonian systems.
• Noise-induced diffusion and modulational diffusion from periodic driving are resonance phenomena.
• The logarithmic dependence of escape time on perturbation amplitude highlights the sensitivity of chaotic systems to external influences.