  We show that the interband dynamics in a tilted two-band Bose-Hubbard model
can be reduced to an analytically accessible spin model in the case of resonant
interband oscillations. This allows us to predict the revival time of these
oscillations which decay and revive due to inter-particle interactions. The
presented mapping onto the spin model and the so achieved reduction of
complexity has interesting perspectives for future studies of many-body
systems.
