On unitary time evolution out of equilibrium

We consider -dimensional quantum systems which for positive times evolve with a timeindependent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the one -point functions of local operators depend on the coefficients of the expansion of the nonequilibrium state on the basis of energy eigenstates. We express in this way the asymptotic offset and show under which conditions oscillations around this value stay undamped at large times. We also show how, in the case of small quenches, the structure of the general results simplifies and reproduces that known perturbatively.