  Bogoliubov's theory states that self-interaction effects in Bose-Einstein
condensates produce a characteristic linear dispersion at low momenta. One of
the curious features of Bogoliubov's theory is that the new quasiparticles in
the system are linear combinations of creation and destruction operators of the
bosons. In exciton-polariton condensates, this gives the possibility of
directly observing the negative branch of the Bogoliubov dispersion in the
photoluminescence (PL) emission. Here we theoretically examine the PL spectra
of exciton-polariton condensates taking into account of reservoir effects. At
sufficiently high excitation densities, the negative dispersion becomes
visible. We also discuss the possibility for relaxation oscillations to occur
under conditions of strong reservoir coupling. This is found to give a
secondary mechanism for making the negative branch visible.
