A sweep through a quantum phase transition by means of a time-dependent external
parameter (e.g., pressure) entails non-equilibrium phenomena associated with a break-
down of adiabaticity: At the critical point, the energy gap vanishes and the response
time diverges. Consequently, the external time-dependence inevitably drives the system
out of equilibrium, i.e., away from the ground state, if we assume zero temperature
initially. In this way, the initial quantum fluctuations are amplified and may become
observable. By means of several examples, mostly based on ultra-cold atoms, possible
effects of these amplified quantum fluctuations are studied and universal features (such
as freezing) are discussed.