  We compute the energy absorbed by a one dimensional system of cold bosonic
atoms in an optical lattice subjected to lattice amplitude modulation periodic
with time. We perform the calculation for the superfluid and the Mott insulator
created by a weak lattice, and the Mott insulator in a strong lattice
potential. For the latter case we show results for 3D systems as well. Our
calculations, based on bosonization techniques and strong coupling methods, go
beyond standard Bogoliubov theory. We show that the energy absorption rate
exhibits distinctive features of low dimensional systems and Luttinger liquid
physics. We compare our results with experiments and find good agreement.
