Complex paths for regular-to-chaotic tunneling rates

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical approach based on complex paths for the prediction of dynamical tunneling rates from regular tori to the chaotic region. This approach is demonstrated for the standard map giving excellent agreement with numerically determined tunneling rates.Comment: 5 pages, 4 figure

Weyl law for open systems with sharply divided mixed phase space

A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions in phase space. For a piecewise linear map, we numerically check the validity of our hypothesis, and find good agreement not only for the case with a sharply divided phase space, but also for the case where tiny island chains surround the main regular island. For the latter case, a non-trivial power law exponent appears in the survival probability of classical escaping orbits, which may provide a clue to develop the Weyl law for more generic mixed systems.Comment: 8 pages, 14 figure

Tunneling Mechanism due to Chaos in a Complex Phase Space

We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features of tunneling perfectly and it enables us to solve all the reasons why those features appear in spite of absence of chaos on the real plane. Multi-generation structure of manifolds, which is the manifestation of complex-domain homoclinic entanglement created by complexified classical dynamics, allows a symbolic coding and it is used as a guiding principle to extract dominant complex trajectories from all the semiclassical candidates.Comment: 4 pages, RevTeX, 6 figures, to appear in Phys. Rev.