  Injection and decay of particles in an inhomogeneous quantum condensate can
significantly change its behaviour. We model trapped, pumped, decaying
condensates by a complex Gross-Pitaevskii equation and analyse the density and
currents in the steady state. With homogeneous pumping, rotationally symmetric
solutions are unstable. Stability may be restored by a finite pumping spot.
However if the pumping spot is larger than the Thomas-Fermi cloud radius, then
rotationally symmetric solutions are replaced by solutions with spontaneous
arrays of vortices. These vortex arrays arise without any rotation of the trap,
spontaneously breaking rotational symmetry.
