  Out of equilibrium quantum systems, on top of quantum fluctuations, display
complex temporal patterns. Such time fluctuations are generically exponentially
small in the system volume and can be therefore safely ignored in most of the
cases. However, if one consider small quench experiments, time fluctuations can
be greatly enhanced. We show that time fluctuations may become stronger than
other forms of equilibrium quantum fluctuations if the quench is performed
close to a critical point. For sufficiently relevant operators the full
distribution function of dynamically evolving observable expectation values,
becomes a universal function uniquely characterized by the critical exponents
and the boundary conditions. At regular points of the phase diagram and for non
sufficiently relevant operators the distribution becomes Gaussian. Our
predictions are confirmed by an explicit calculation on the quantum Ising
model.
