  Determining the role of initial conditions in the late time evolution is a
key issue for the theory of nonequilibrium dynamics of isolated quantum
systems. Here we extend the theory of quantum quenches to the case in which
before the quench the system is in an excited state. In particular, we show
perturbatively in the size of the quench (and for arbitrarily strong
interactions among the quasiparticles) that persistent oscillations of
one-point functions require the presence of a one-quasiparticle contribution to
the nonequilibrium state, as originally shown in [J. Phys. A 47 (2014) 402001]
for the quenches from the ground state. Also in the present case, we argue that
the results generically have nonperturbative implications. Oscillations staying
undamped within the accessible time interval, far beyond the perturbative time
scale, are nowadays observed in numerical simulations.
