  We study the decay of survival probability at quantum phase transitions
(QPT). The semiclassical theory is found applicable in the vicinities of
critical points with infinite degeneracy. The theory predicts a power law decay
of the survival probability for relatively long times in systems with d=1 and
an exponential decay in systems with sufficiently large d, where d is the
degrees of freedom of the underlying classical dynamics. The semiclassical
predictions are checked numerically in four models.
