  Using a Luttinger liquid theory we investigate the time evolution of the
particle density of a one-dimensional fermionic system with open boundaries and
subject to a finite duration quench of the inter-particle interaction. We
provide analytical and asymptotic solutions to the unitary time evolution of
the system, showing that both switching on and switching off the quench ramp
create light-cone perturbations in the density. The post-quench dynamics is
strongly affected by the interference between these two perturbations. In
particular, we find that the discrepancy between the time-dependent density and
the one obtained by a generalized Gibbs ensemble picture vanishes with an
oscillatory behavior as a function of the quench duration, with local minima
corresponding to a perfect overlap of the two light-cone perturbations. For
adiabatic quenches, we also obtain a similar behavior in the approach of the
generalized Gibbs ensemble density towards the one associated with the ground
state of the final Hamiltonian.
