  Time dynamics of isolated many-body quantum systems has long been an elusive
subject. Very recently, however, meaningful experimental studies of the problem
have finally become possible, stimulating theoretical interest as well.
Progress in this field is perhaps most urgently needed in the foundations of
quantum statistical mechanics. This is so because in generic isolated systems,
one expects nonequilibrium dynamics on its own to result in thermalization: a
relaxation to states where the values of macroscopic quantities are stationary,
universal with respect to widely differing initial conditions, and predictable
through the time-tested recipe of statistical mechanics. However, it is not
obvious what feature of many-body quantum mechanics makes quantum
thermalization possible, in a sense analogous to that in which dynamical chaos
makes classical thermalization possible. For example, dynamical chaos itself
cannot occur in an isolated quantum system, where time evolution is linear and
the spectrum is discrete. Underscoring that new rules could apply in this case,
some recent studies even suggested that statistical mechanics may give wrong
predictions for the outcomes of relaxation in such systems. Here we demonstrate
that an isolated generic quantum many-body system does in fact relax to a state
well-described by the standard statistical mechanical prescription. Moreover,
we show that time evolution itself plays a merely auxiliary role in relaxation
and that thermalization happens instead at the level of individual eigenstates,
as first proposed by J.M. Deutsch and M. Srednicki. A striking consequence of
this eigenstate thermalization scenario is that the knowledge of a single
many-body eigenstate suffices to compute thermal averages-any eigenstate in the
microcanonical energy window will do, as they all give the same result.
