  We study analytically and numerically quench dynamics and defects formation
in the quantum Ising model in the presence of a time-dependent transverse
magnetic field. We generalize the Landau-Ziner formula to the case of
non-adiabatic evolution of the quantum system. For a quasi-static magnetic
field, with a slow dependence on time, our outcomes are similar to the results
predicted by the Landau-Zener formula. However, a quench dynamics under a
shock-wave load is more complicated. The final state of the system depends on
the amplitude and pulse velocity, resulting in the mixture of ground and
excited states and significant density of defects.
