Lattice bosons in a quasi-disordered environment: The effects of a superlattice potential on single particle and many particle properties

In this paper we present a theoretical investigation of the effect of a superlattice potential on some properties of non-interacting bosons in one dimensional lattices with Aubry-And\'re disorder potential. In the first part, we investigate the single particle localization properties. We find a re-entrant localization-delocalization transition and the development of multiple mobility edges for a range of superlattice potential strengths. In the second part, we study the Bose-Einstein condensation with an additional harmonic trapping potential. We find that an increase in the superlattice potential leads to an increase in the depletion of the condensate in the low temperature limit.