  We investigate dynamical stability of the ground state against a
time-periodic and spatially-inhomogeneous magnetic field for finite quantum XXZ
spin chains. We use the survival probability as a measure of stability and
demonstrate that it decays as $P(t) \propto t^{-1/2}$ under a certain
condition. The dynamical properties should also be related to the level
statistics of the XXZ spin chains with a constant spatially-inhomogeneous
magnetic field. The level statistics depends on the anisotropy parameter and
the field strength. We show how the survival probability depends on the
anisotropy parameter, the strength and frequency of the field.
