Condensation of microcavity polaritons and the substantial influence ofpair-breaking disorder and decoherence leading to a laser regime has beenrecently considered using two different models: a model for direct two bandexcitons in a disordered quantum well coupled to light and a model where thecavity mode couples instead to a medium of localised excitons, represented bytwo-level oscillators in the presence of dephasing processes. Even ifcomplementary from the point of view of assumptions, the models share most ofthe main conclusions and show similar phase diagrams. The issue whetherexcitons are propagating or localised seems secondary for the polaritoncondensation and the way in which pair-breaking disorder and decoherenceprocesses influence the condensation and drive the microcavity into a lasingregime is, within the approximations used in each model, generic. The reasonsfor the similarities between the two physical situations are analysed andexplained.
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