  We review recent progress in the nonequilibrium dynamics of thermally
isolated many-body quantum systems, evolving with an ensemble of Hamiltonians
as opposed to deterministic evolution with a single time-dependent Hamiltonian.
Such questions arise in (i) quantum dynamics of disordered systems, where
different realizations of disorder give rise to an ensemble of real-time
quantum evolutions. (ii) quantum evolution with noisy Hamiltonians (temporal
disorder), which leads to stochastic Schrodinger equations, and, (iii) in the
broader context of quantum optimal control, where one needs to analyze an
ensemble of permissible protocols in order to find one that optimizes a given
figure of merit. The theme of ensemble quantum evolution appears in several
emerging new directions in noneqilibrium quantum dynamics of thermally isolated
many-body systems, which include many-body localization, noise-driven systems,
and shortcuts to adiabaticity.
