  In this paper we examine the excitations observable in atoms confined in an
optical lattice around the superfluid-insulator transition. We use increases in
the number variance of atoms, subsequent to tilting the lattice as the primary
diagnostic of excitations in the lattice. We show that this locally determined
quantity should be a robust indicator of coherence changes in the atoms
observed in recent experiments. This was found to hold for commensurate or
non-commensurate fillings of the lattice, implying our results will hold for a
wide range of physical cases. Our results are in good agreement with the
quantitative factors of recent experiments. We do, howevers, find extra
features in the excitation spectra. The variation of the spectra with the
duration of the perturbation also turns out to be an interesting diagnostic of
atom dynamics.
