  In general, isolated integrable quantum systems have been found to relax to
an apparent equilibrium state in which the expectation values of few-body
observables are described by the generalized Gibbs ensemble. However, recent
work has shown that relaxation to such a generalized statistical ensemble can
be precluded by localization in a quasiperiodic lattice system. Here we
undertake complementary single-particle and many-body analyses of
noninteracting spinless fermions and hard-core bosons within the Aubry-Andre
model to gain insight into this phenomenon. Our investigations span both the
localized and delocalized regimes of the quasiperiodic system, as well as the
critical point separating the two. Considering first the case of spinless
fermions, we study the dynamics of the momentum distribution function and
characterize the effects of real-space and momentum-space localization on the
relevant single-particle wave functions and correlation functions. We show that
although some observables do not relax in the delocalized and localized
regimes, the observables that do relax in these regimes do so in a manner
consistent with a recently proposed Gaussian equilibration scenario, whereas
relaxation at the critical point has a more exotic character. We also construct
various statistical ensembles from the many-body eigenstates of the fermionic
and bosonic Hamiltonians and study the effect of localization on their
properties.
