The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-André Hamiltonian. This, in turn, presents a localization transition that has been observed in recent experiments using ultracold atoms or light. It is shown here that, in contrast to the Anderson model, the localization mechanism has a classical origin, namely it is not due to a quantum suppression of a classically allowed transport process, but rather is produced by a trapping by the potential. Explicit comparisons with the Anderson model as well as with experiments are presented.

• Received 14 May 2009

DOI:https://doi.org/10.1103/PhysRevA.81.013614