  We study the interplay between coherent transport by tunneling and diffusive
transport through classically chaotic phase-space regions, as it is reflected
in the Floquet spectrum of the periodically driven quartic double well. The
tunnel splittings in the semiclassical regime are determined with high
numerical accuracy, and the association of the corresponding doublet states to
either chaotic or regular regions of the classical phase space is quantified in
terms of the overlap of the Husimi distribution with the chaotic layer along
the separatrix. We find a strong correlation between both quantities. They show
an increase by orders of magnitude as chaotic diffusion between the wells
starts to dominate the classical dynamics. We discuss semiclassical
explanations for this correlation.
