  We drive the one-dimensional quantum Ising chain in the transverse field from
the paramagnetic phase to the critical point and study its free evolution
there. We analyze excitation of such a system at the critical point and
dynamics of its transverse magnetization and Loschmidt echo during free
evolution. We discuss how the system size and quench-induced scaling relations
from the Kibble-Zurek theory of non-equilibrium phase transitions are encoded
in quasi-periodic time evolution of the transverse magnetization and Loschmidt
echo.
