After a sudden quench, the dynamics and thermalization of isolated
quantum systems are topics that have generated increasing attention in recent
years. This is in part motivated be the desire of gaining a deeper
understanding of how statistical behavior emerges out of the unitary evolution
in isolated quantum systems and in part by novel experiments with ultracold
gases. Several studies have found that while unitary dynamics in generic
systems lead to thermal behavior of observables after relaxation, the same is
not true for integrable systems. The latter need to be described using
generalized ensembles, which take into account the existence of relevant sets
of conserved quantities. In this talk, we discuss how delocalization-to-
localization transitions in integrable and nonintegrable disordered quantum
systems change the picture above. We find that the relaxation dynamics,
whenever relaxation takes place, is close to power law in those systems. In
addition, statistical mechanics descriptions (standard or generalized) break
drown in the localized regimes. We discuss how this relates to the failure of
eigenstate thermalization in the presence of localization.
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