  We consider $d$-dimensional quantum systems which for positive times evolve
with a time-independent 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.
