  We develop a nanoscale dynamical mean-field theory (nano-DMFT) to deal with
strong Coulomb interaction effects in physical systems that are intermediate in
size between atoms and bulk materials, taking into account the tunneling into
nearby electrodes. Focusing on a simplified treelike geometry, the usual DMFT
loop simply stops when the finite lattice is fully covered, starting with an
initial seed provided by the electronic environment at the boundary. To
illustrate this nano-DMFT, we investigate the disappearance of the
quasiparticle weight in a correlated nano object near the Mott transition. In
contrast to thermally driven classical phase transitions, quantum effects lead
to unexpected oscillations of the order parameter, related to the interference
of coherent renormalized quasiparticles. This behavior also implies a spatially
inhomogeneous Mott localization process at the nanoscale.
