Dynamical structure factor of one dimensional bosons in optical lattices

We investigate a one dimensional system of cold bosonic atoms in an optical lattice subjected to a time dependent periodic potential. We study the dynamic structure factor and the excitation spectrum in different regimes: superfluid and Mott insulator. In particular the strong interactions gives rise to a continuum of excitations in the superfluid phase. We discuss the application to recent experiments on bosonic tubes. We also discuss comparisons to higher dimension situations.