  We study the ground-state properties and nonequilibrium dynamics of hard-core
bosons confined in one-dimensional lattices in the presence of an additional
periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed
after a sudden switch-on or switch-off of the superlattice potential, which can
bring the system into insulating or superfluid phases, respectively. A collapse
and revival of the zero-momentum peak can be seen in the first case. We study
in detail the relaxation of these integrable systems towards equilibrium. We
show how after relaxation time averages of physical observables, like the
momentum distribution function, can be predicted by means of a generalization
of the Gibbs distribution.
