Disordered bosons: Condensate and excitations

The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schrödinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed in porous media.