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

Phys Rev Lett. 2010 Mar 19;104(11):114101. doi: 10.1103/PhysRevLett.104.114101. Epub 2010 Mar 16.


We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given variant Planck's over 2pi regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.