Phase space transport in noisy Hamiltonian systems

Area of Science:

• * Hamiltonian dynamics
• * Statistical mechanics
• * Nonlinear dynamics

Background:

• * Hamiltonian systems with global stochasticity can exhibit slow phase space transport.
• * Obstructions like cantori and Arnold webs impede the exploration of phase space.
• * Understanding transport mechanisms is crucial for statistical mechanics and dynamical systems theory.

Purpose of the Study:

• * To investigate the impact of low-amplitude friction and noise on phase space transport.
• * To quantify the acceleration of transport rates due to non-Hamiltonian perturbations.
• * To analyze the role of perturbation details, friction, and noise amplitude on transport.

Main Methods:

• * Numerical simulations of time-independent Hamiltonian systems.
• * Analysis of ensembles of orbits and their phase space trajectories.
• * Calculation of first passage times through cantori and other phase space structures.

Main Results:

• * Weak non-Hamiltonian perturbations dramatically increase the rate of phase space transport.
• * Perturbations accelerate the penetration of cantori and Arnold webs.
• * The rate of approach to an invariant measure is significantly enhanced.
• * The detailed form of white noise perturbations is unimportant for transport.
• * Friction has minimal impact on the accelerated transport.
• * The response amplitude to weak noise scales logarithmically with noise amplitude.

Conclusions:

• * Low-amplitude noise and friction can be highly effective in accelerating phase space transport.
• * The precise nature of the perturbation is less critical than its presence for enhancing transport.
• * Logarithmic scaling of response amplitude with noise amplitude provides a quantitative understanding of the effect.