  We present evidence that tunneling processes in near-integrable systems are
enhanced due to the manifestation of nonlinear resonances and their respective
island chains in phase space. A semiclassical description of this
"resonance-assisted" mechanism is given, which is based on a local perturbative
description of the dynamics in the vicinity of the resonances. As underlying
picture, we obtain that the quantum state is coupled, via a succession of
classically forbidden transitions across nonlinear resonances, to high
excitations within the well, from where tunneling occurs with a rather large
rate. The connection between this description and the complex classical
structure of the underlying integrable dynamics is furthermore studied, giving
ground to the general coherence of the description as well as guidelines for
the identification of the dominant tunneling paths. The validity of this
mechanism is demonstrated within the kicked Harper model, where good agreement
between quantum and semiclassical (resonance-assisted) tunneling rates is
found.
