  We consider the question of thermalization for isolated quantum systems after
a sudden parameter change, a so-called quantum quench. In part icular we
investigate the pre-requisites for thermalization focusing on the statistical
properties of the time-averaged density matrix and o f the expectation values
of observables in the final eigenstates. We find that eigenstates, which are
rare compared to the typical ones sampled by the micro-canonical distribution,
are responsible for the absence of thermalization of some infinite integrable
models and play an important role for some non-integrable systems of finite
size, such as the Bose-Hubbard model. We stress the importance of finite size
effects for the thermalization of isolated quantum systems and discuss two
alternative scenarios for thermalization, as well as ways to prune down the
correct one.
