  Several recent studies have investigated the dynamics of cold atoms in
optical lattices subject to AC forcing; the theoretically predicted
renormalization of the tunneling amplitudes has been verified experimentally.
Recent observations include global motion of the atom cloud, such as giant
"Super-Bloch Oscillations" (SBOs). We show that, in order to understand
unexplained features of SBOs, in addition to the renormalization of the
tunneling, a new and important phase correction must be included. For Fermionic
systems with strong attractive interactions, one may engineer different types
of collisions and recollisions between bound-pairs and unpaired atoms.
