Semiclassical Approach to Survival Probability at Quantum Phase Transitions

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.