Semiclassical approach to survival probability at quantum phase transitions.

We study the decay of survival probability at quantum phase transitions with infinitely degenerate ground levels at critical points. For relatively long times, the semiclassical theory predicts power-law decay of the survival probability in systems with d=1 and exponential decay in systems with sufficiently large d, where d is the degrees of freedom of the classical counterpart of the system. The predictions are checked numerically in four models.