Résumé
We study the strong localization of atomic matter waves in a disordered potential created by atoms pinnedat the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localizationlength of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3Dsystem), are numerically investigated as a function of the effective scattering length between the atomic matterwave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting featuresof the density of states are discovered at negative energies, where maxima in the density of bound states for thesystem can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers.In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies,the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge isfound, and a rapid exponential-like increase of the localization length is observed at high energy.