Localization transition in weakly interacting Bose superfluids in one-dimensional quasiperdiodic lattices

We study the localization of collective pair excitations in weakly interacting Bose superfluids in one-dimensional quasiperiodic lattices. The localization diagram is first determined numerically. For intermediate interaction and quasiperiodic amplitude we find a sharp localization transition, with extended low-energy states and localized high-energy states. We then develop an analytical treatment, which allows us to quantitatively map the localization transition into that of an effective multiharmonic quasiperiodic system.