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We examine the one-dimensional Gross-Pitaevskii lattice at zero temperaturein the presence of uncorrelated disorder. We obtain analytical expressions forthe thermodynamic properties of the ground state field and compare them withnumerical simulations both in the weak and strong interaction regimes. Weanalyze weak excitations above the ground state and compute the localizationproperties of Bogoliubov-de Gennes modes. In the long-wavelength limit, thesemodes delocalize in accordance with the extended nature of the ground state.For strong interactions, we observe and derive a divergence of theirlocalization length at finite energy due to an effective correlated disorderinduced by the weak ground state field fluctuations. We derive effective stronginteraction field equations for the excitations and generalize to higherdimensions.

Anderson localization of excitations in disordered Gross-Pitaevskii lattices