In typical Hamiltonian systems regions of regular and chaotic motion coexist within a mixed phase space. While they are strictly separated in classical mechanics, dynamical tunneling allows quantum states to penetetrate classical inaccessible regions in phase space. We present a semiclassical picture for this regular-to-chaotic tunneling process, which also captures the resonance-assisted enhancement due to a nonlinear resonance chain in the classical phase space. Within an integrable approximation with one nonlinear resonance chain we identify complex paths for direct and resonance-assisted tunneling. Using WKB techniques we obtain tunneling rates from this paths. In particular the resonance-assisted contribution can be evaluated analytically and leads to a prediction based on just a few properties of the classical phase space. We illustrate our approach with the paradigmatic model of the standard map where excellent agreement with numerically determined tunneling rates is observed.

* Felix Fritzsch, TU Dresden