  In generic Hamiltonian systems tori of regular motion are dynamically
separated from regions of chaotic motion in phase space. Quantum mechanically
these phase-space regions are coupled by dynamical tunneling. We introduce a
semiclassical approach based on complex paths for the prediction of dynamical
tunneling rates from regular tori to the chaotic region. This approach is
demonstrated for the standard map giving excellent agreement with numerically
determined tunneling rates.
