  A second order phase transition induced by a rapid quench can lock out
topological defects with densities far exceeding their equilibrium expectation
values. We use quantum kinetic theory to show that this mechanism, originally
postulated in the cosmological context, and analysed so far only on the mean
field classical level, should allow spontaneous generation of vortex lines in
trapped Bose-Einstein condensates of simple topology, or of winding number in
toroidal condensates.
