  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.
