  We present a two-band Bose-Hubbard model which is shown to be minimal in the
necessary coupling terms at resonant tunneling conditions. The dynamics of the
many-body problem is studied by sweeping the system across an avoided level
crossing. The linear sweep generalizes Landau-Zener transitions from
single-particle to many-body realizations. The temporal evolution of single-
and two-body observables along the sweeps is investigated in order to
characterize the non-equilibrium dynamics in our complex quantum system.
