  We investigate equilibration and generalized thermalization of the quantum
Harmonic chain under local quantum quench. The quench action we consider is
connecting two disjoint harmonic chains of different sizes and the system jumps
between two integrable settings. We verify the validity of the Generalized
Gibbs Ensemble description for this infinite dimensional Hilbert space system
and also identify equilibration between the subsystems as in classical systems.
Using Bogoliubov transformations, we show that the eigenstates of the system
prior to the quench evolve towards the Gibbs Generalized Ensemble description.
Eigenstates that are more delocalized (in the sense of inverse participation
ratio) prior to the quench, tend to equilibrate more rapidly. Further, through
the phase space properties of a Generalized Gibbs Ensemble and the strength of
stimulated emission, we identify the necessary criterion on the initial states
for such relaxation at late times and also find out the states which would
potentially not be described by the Gibbs Generalized Ensemble description.
