Level broadening effects in quantum kinetic equations: Hot luminescence from a quantum wire near the optical phonon emission threshold

A recipe for the generalization of the Boltzmann equation to a quantum kinetic equation is given for cases in which only level shift and broadening are considered, while coherence phenomena can be neglected. We also consider a specific problem: Hot luminescence from a quantum wire near the threshold for optical phonon emission. The problem is first discussed within the framework of the Boltzmann equation. After pointing out the failure of this description, the Boltzmann equations are generalized to a set of quantum kinetic equations, which in turn are solved in order to describe the luminescence spectra.