  Using inhomogeneous dynamical mean-field theory, we argue that the
normal-metal proximity effect forces any finite number of "barrier" planes that
are described by the (paramagnetic) Hubbard model and sandwiched between
semi-infinite metallic leads to always be a Fermi liquid at T=0. This then
implies that the inhomogeneous system restores lattice periodicity at zero
frequency, has a well-defined Fermi surface, and should display perfect
(ballistic) conductivity or "transparency". These results are, however, fragile
with respect to finite frequency, V, T, disorder, or magnetism, all of which
restore the expected quantum tunneling regime through a finite-width Mott
insulator. Our formal results are complemented by numerical renormalization
group studies on small thickness barriers that illustrate under what
circumstances this behavior might be seen in real experimental systems.
