  Cold atoms in optical lattices allow for accurate studies of many body
dynamics. Rapid time-dependent modifications of optical lattice potentials may
result in significant excitations in atomic systems. The dynamics in such a
case is frequently quite incompletely described by standard applications of
tight-binding models (such as e.g. Bose-Hubbard model or its extensions) that
typically neglect the effect of the dynamics on the transformation between the
real space and the tight-binding basis. We illustrate the importance of a
proper quantum mechanical description using a multi-band extended Bose-Hubbard
model with time-dependent Wannier functions. We apply it to situations,
directly related to experiments.
