  Here we give detailed derivations and provide additional examples to the main
paper: arXiv:0706.0212. In particular, we discuss the scaling behavior of
observables like correlation functions and density of excitations. We also
analyze effects of nonintegrability of the Bose-Hubbard model on the long-time
dynamics of the correlation functions. In addition we explicitly consider
several interacting models, where we are able to analyze slow dynamics and
classify it according to the regimes suggested in the main paper.
