  We provide an account of the static and dynamic properties of hard-core
bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic
potential for which the single-particle spectrum has mobility edges. We use the
mapping from strongly interacting bosons to weakly interacting fermions, and
provide exact numerical results for hard-core bosons in and out of equilibrium.
In equilibrium, we find that the system behaves like a quasi-condensate
(insulator) depending on whether the Fermi surface of the corresponding
fermionic system lies in a spectral region where the single-particle states are
delocalized (localized). We also study non-equilibrium expansion dynamics of
initially trapped bosons, and demonstrate that the extent of partial
localization is determined by the single-particle spectrum.
