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I.V. Sideris, H.E. Kandrup (University of Florida)
An investigation of the effects of low amplitute noise and periodic driving on phase space transport in three-dimensional Hamiltonian systems will be presented. This is a problem directly applicable to stellar systems like elliptical galaxies, where the perturbations are generated by internal irregularities (graininess) or a surrounding environment (e.g. companion galaxies). A number of experiments were used to study how small perturbations of individual orbits can dramatically accelerate phase space transport. Discreteness effects were idealised as white noise, internal oscillations and the effects of companion objects were idealised as low amplitude periodic driving and the effect of the surrounding environment as coloured noise. This acceleration allows sticky chaotic orbits, which are trapped in regions of the phase space near regular islands, to become untrapped on surprisingly short time scales. The effects of small perturbations were also examined in the context of orbit ensembles in order to understand if and how the efficacy of chaotic mixing increases. For both noise and periodic driving the effect scales roughly logarithmically with amplitude. The experimental results suggest strongly that, like periodic driving, noise-induced phase space acceleration is a resonance phenomenon, which involves coupling between the frequencies at which the noise has substantial power and the natural frequencies of the unperturbed orbit. For white noise the details are not important since both additive and multiplicative noise seem to give similar results. This means that we can ignore complications which are nearly inaccessible observationally. For colored noise the only thing that matters is whether there is substantial power in frequencies comparable to the natural frequencies of the orbits.
This research was supported in part by NSF AST-0070809 and by the Institute for Geophysics and Planetary Physics at Los Alamos National Laboratory.