  We investigate the disorder-induced localization transition in Bose-Einstein
condensates for the Anderson and Aubry-Andre models in the non-interacting
limit using exact diagonalization. We show that, in addition to the standard
superfluid fraction, other tools such as the entanglement and fidelity can
provide clear signatures of the transition. Interestingly, the fidelity
exhibits good sensitivity even for small lattices. Effects of the system size
on these quantities are analyzed in detail, including the determination of a
finite-size-scaling law for the critical disorder strength in the case of the
Anderson model.
