In this presentation I present the theory of phonon-assisted luminescence, in terms of non-equilibrium  Green’s functions and time-dependent perturbation theory. We derived a simple formule for light emission in the limit of low excited carriers including excitonic effects and then included coupling with phonons by time-dependent perturbation theory. This approach is then applied to the study of luminescence in hexagonal boron nitride.

Here the link to the presentation.

All the analytic derivations can be found here: https://arxiv.org/abs/1807.11797