Propagation of collective pair excitations in disordered Bose superfluids

We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local-density depletion induced by strong disorder at the mean-field level and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly nonmonotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.