  Condensation of microcavity polaritons and the substantial influence of
pair-breaking disorder and decoherence leading to a laser regime has been
recently considered using two different models: a model for direct two band
excitons in a disordered quantum well coupled to light and a model where the
cavity mode couples instead to a medium of localised excitons, represented by
two-level oscillators in the presence of dephasing processes. Even if
complementary from the point of view of assumptions, the models share most of
the main conclusions and show similar phase diagrams. The issue whether
excitons are propagating or localised seems secondary for the polariton
condensation and the way in which pair-breaking disorder and decoherence
processes influence the condensation and drive the microcavity into a lasing
regime is, within the approximations used in each model, generic. The reasons
for the similarities between the two physical situations are analysed and
explained.
