  Dynamical phase transitions can occur in isolated quantum systems that are
brought out of equilibrium by sudden parameter changes. We discuss the
characterization of such dynamical phase transitions based on the statistics of
produced excitations. We consider both the O(N) model in the large N limit and
a spin model with long range interactions and show that the dynamical
criticality of their prethermal steady-states manifests most dramatically not
in the average number of excitations but in their higher moments. We argue that
the growth of defect fluctuations carries unique signatures of the dynamical
criticality, irrespective of the precise details of the model. Our theoretical
results should be relevant to quantum quench experiments with ultracold bosonic
atoms in optical lattices.
