  First passage time experiments were used to explore the effects of low
amplitude noise as a source of accelerated phase space diffusion in
two-dimensional Hamiltonian systems, and these effects were then compared with
the effects of periodic driving. The objective was to quantify and understand
the manner in which ``sticky'' chaotic orbits that, in the absence of
perturbations, are confined near regular islands for very long times, can
become ``unstuck'' much more quickly when subjected to even very weak
perturbations. For both noise and periodic driving, the typical escape time
scales logarithmically with the amplitude of the perturbation. For white noise,
the details seem unimportant: Additive and multiplicative noise typically have
very similar effects, and the presence or absence of a friction related to the
noise by a Fluctuation-Dissipation Theorem is also largely irrelevant. Allowing
for colored noise can significantly decrease the efficacy of the perturbation,
but only when the autocorrelation time becomes so large that there is little
power at frequencies comparable to the natural frequencies of the unperturbed
orbit. Similarly, periodic driving is relatively inefficient when the driving
frequency is not comparable to these natural frequencies. This suggests
strongly that noise-induced extrinsic diffusion, like modulational diffusion
associated with periodic driving, is a resonance phenomenon. The logarithmic
dependence of the escape time on amplitude reflects the fact that the time
required for perturbed and unperturbed orbits to diverge a given distance
scales logarithmically in the amplitude of the perturbation.
