  In this paper, a non-Markovian Gross-Pitaevskii equation is proposed to
describe the formation of a condensate in an exciton-polariton system under
incoherent pumping. By introducing spatially delta-correlated noise terms, we
observe a transition from a spatially ordered phase to a disordered one as the
temperature increases. In course of this process, the population of the
condensate is significantly reduced. Irregularly located separate dense spots
of condensate above the transition temperature are revealed. Using the Gabor
transform, it is shown that, with increasing temperature, the condensate
decoheres, that is accompanied by the transition from narrowband to broadband
spectral density.
