Regular-to-chaotic tunneling rates using a fictitious integrable system

Phys Rev Lett. 2008 Mar 14;100(10):104101. doi: 10.1103/PhysRevLett.100.104101. Epub 2008 Mar 13.

Abstract

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the island. For the standard map and other kicked systems we find agreement with numerical results for all regular states in a regime where resonance-assisted tunneling is not relevant.