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 prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ionization rates and quality factors.