Statistical redistribution of trajectories from a torus to tori by chaotic dynamical tunneling

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Abstract
The effect of chaos in dynamical tunneling that induces a transition among tori in a near integrable system is investigated. Even though a system energy is moderately low enough for a quasiseparatrix to be sufficiently thin, in other words, even if most of the phase space is filled with invariant tori, tunneling paths that connect the tori can be strongly chaotic. A direct consequence of the chaos is manifested as a mixing property of the tunneling paths, which in turn brings about a statistical redistribution of classical trajectories after the tunneling, that is, the probability for a trajectory to be found on a given torus after the tunneling is nearly proportional to the corresponding area on the Poincaré surface of section. This is highly analogous to the principle of equipartition in statistical mechanics. © 1996 The American Physical Society.