  The concept of the macroscopic wave function is a key for understanding
macroscopic quantum phenomena. The existence of this object reflects a certain
order, as is present in a Bose-Einstein condensate when a single-particle
orbital is occupied by a macroscopic number of bosons. We extend these ideas to
situations in which a condensate is acted on by an explicitly time-dependent
force. While one might assume that such a force would necessarily degrade any
pre-existing order, we demonstrate that macroscopic wave functions can persist
even under strong forcing. Our definition of the time-dependent order parameter
is based on a comparison of the evolution of $N$-particle states on the one
hand, and of states with $N - 1$ particles on the other. Our simulations
predict the possibility of an almost instantaneous dynamical destruction of a
macroscopic wave function under currently accessible experimental conditions.

Quantum Gases