  We investigate by means of the time-dependent Gutzwiller approximation the
transport properties of a strongly-correlated slab subject to Hubbard repulsion
and connected with to two metallic leads kept at a different electrochemical
potential. We focus on the real-time evolution of the electronic properties
after the slab is connected to the leads and consider both metallic and Mott
insulating slabs. When the correlated slab is metallic, the system relaxes to a
steady-state that sustains a finite current. The zero-bias conductance is
finite and independent of the degree of correlations within the slab as long as
the system remains metallic. On the other hand, when the slab is in a Mott
insulating state, the external bias leads to currents that are exponentially
activated by charge tunneling across the Mott-Hubbard gap, consistent with the
Landau-Zener dielectric breakdown scenario.
