Regular-to-chaotic tunneling rates: From the quantum to the semiclassical regime

In systems with a mixed phase space, regular islands are dynamically separated from the chaotic sea, while quantum mechanically these phase-space regions are connected by dynamical tunneling. We derive a prediction of dynamical tunneling rates of regular states to the chaotic sea by combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. For systems with one or multiple dominant nonlinear resonances we find excellent agreement to numerics.