  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 (in the thermodynamic limit).
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 can be drastically
amplified and may become observable -- especially for symmetry-breaking
(restoring) transitions. By means of several examples, possible effects of
these amplified quantum fluctuations are studied and universal features (such
as freezing) are discussed.
