Recent developments in macroscopic quantum electrodynamics

We review two recent developments in constructive macroscopic quantum electrodynamics. These concern the derivation of the large-scale dynamical properties of plasma and laser models from their underlying quantum structures. In the case of the plasma model, consisting of a non-relativistic system of electrons coupled to a quantised electromagnetic field, we show that the macroscopic dynamics is governed by classical Vlasov-Maxwell equations and supports transitions from deterministic to stochastic flows. In the case of the laser model, which is a new version of that of Hepp and Lieb [8], recast within the framework of quantum dynamical semigroups, we obtain a generalisation of the HL theory and show that it supports optically chaotic phases, as well as the usual quiescent and coherent ones.