  We study the non-equilibrium dynamics of a one-dimensional system of hard
core bosons (HCBs) in the presence of an onsite potential (with an alternating
sign between the odd and even sites) which shows a quantum phase transition
(QPT) from the superfluid (SF) phase to the so-called "Mott Insulator" (MI)
phase. The ground state quantum fidelity shows a sharp dip at the quantum
critical point (QCP) while the fidelity susceptibility shows a divergence right
there with its scaling given in terms of the correlation length exponent of the
QPT. We then study the evolution of this bosonic system following a quench in
which the magnitude of the alternating potential is changed starting from zero
(the SF phase) to a non-zero value (the MI phase) according to a half Rosen
Zener (HRZ) scheme or brought back to the initial value following a full Rosen
Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the
final MI phase (following the HRZ quench) and is found to be less than the
equilibrium value ($\log 2$) due to the defects generated in the final state as
a result of the quenching starting from the QCP of the system. We also briefly
dwell on the FRZ quenching scheme in which the system is finally in the SF
phase through the intermediate MI phase and calculate the reduction in the
supercurrent and the non-zero value of the residual local entropy density in
the final state. Finally, the loss of coherence of a qubit (globally and weekly
coupled to the HCB system) which is initially in a pure state is investigated
by calculating the time-dependence of the decoherence factor when the HCB chain
evolves under a HRZ scheme starting from the SF phase. This result is compared
with that of the sudden quench limit of the half Rosen-Zener scheme where an
exact analytical form of the decoherence factor can be derived.
