Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems

Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems.

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a nonperturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling....

Resonance-assisted tunneling in mixed regular-chaotic systems

Complex-path prediction of resonance-assisted tunneling in mixed systems.

We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a predictio...

Resonance-assisted tunneling in near-integrable systems.

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting betwee...

Periodic Orbit Quantization of Mixed Regular Chaotic Systems

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence function up to, in principle, infinite length. As in our recent work the recurrence signal is inverted by means of a high resolution spectral analyzer (harmonic i...