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We demonstrate that in quantum-dot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both loss mechanisms strongly affects the transition from the weak to the strong coupling regime as well as the shape of Mollow-type spectra in untypical ways. For weak coupling, where the spectra degenerate to a single line, we predict that their widths decrease with rising temperature.

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