Ionization via Chaos Assisted Tunneling

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity via chaotic diffusion. The specific system is realistic : it is the hydrogen atom exposed to either linearly or circularly polarized microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar statistical fluctuation properties of the energy and the ionization rate, especially to enhanced fluctuations compared to the purely chaotic case. An appropriate random matrix model, whose predictions are analytically derived, describes accurately these statistical properties.Comment: 30 pages, 11 figures, RevTeX and postscript, Physical Review E in pres

Synchronization in driven versus autonomous coupled chaotic maps

The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction. It is shown that chaotic synchronized states in both systems are equivalent, but the collective states arising after the chaotic synchronized state becomes unstable can be different in these two systems. It is found that the external drive induces chaotic synchronization as well as synchronization of unstable periodic orbits of the local dynamics in the driven lattice. On the other hand, the addition of a global interaction in the autonomous system allows for chaotic synchronization that is not possible in a large coupled map system possessing only local couplings.Comment: 4 pages, 3 figs, accepted in Phys. Rev.