  Quantum tunneling in the presence of chaos is analyzed, focusing especially
on the interplay between quantum tunneling and dynamical localization. We
observed flooding of potentially existing tunneling amplitude by adding noise
to the chaotic sea to attenuate the destructive interference generating
dynamical localization. This phenomenon is related to the nature of complex
orbits describing tunneling between torus and chaotic regions. The tunneling
rate is found to obey a perturbative scaling with noise intensity when the
noise intensity is sufficiently small and then saturate in a large noise
intensity regime. A relation between the tunneling rate and the localization
length of the chaotic states is also demonstrated. It is shown that due to the
competition between dynamical tunneling and dynamical localization, the
tunneling rate is not a monotonically increasing function of Planck's constant.
The above results are obtained for a system with a sharp border between torus
and chaotic regions. The validity of the results for a system with a smoothed
border is also explained.
