Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach

We review the fictitious integrable system approach which predicts dynamical tunneling rates from regular states to the chaotic region in systems with a mixed phase space. It is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the regular island. We focus on the direct regular-to-chaotic tunneling process which dominates, if nonlinear resonances within the regular island are not relevant. For quantum maps, billiard systems, and optical microcavities we find excellent agreement with numerical rates for all regular states.