Anderson localization transitions with and without random potentials

Anderson localization of noninteracting particles has traditionally been viewed as being due to random potentials. However, random potentials are not needed, and localization due to nonrandom quasiperiodic potentials is well studied in one dimension. The authors extend this work to higher dimensions. A quantum particle in a quasiperiodic potential in three dimensions has three ``eigenstate phases'': a localized phase at strong potential, a ballistic phase at weak potential, and a diffusive phase in between. They find that the universality class of the Anderson localization transitions in three dimensions is insensitive to whether or not the potential is random, which is not true in fewer dimensions.