e study theoretically, the photoluminescence properties of a single quantum dot in a microcavity under incoherent excitation. We propose a microscopic quantum statistical approach providing a Lindblad (thus completely positive) description of pumping and decay mechanisms of the quantum dot and of the cavity mode. Our analytical results show that strong coupling (SC) and linewidths are largely independent on the pumping intensity (until saturation effects come into play), in contrast to previous theoretical findings. We shall show the reliable predicting character of our theoretical framework in the analysis of various recent experiments.
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