I am studying a little about QED in a cavity. I don't really understand Vacuum Rabi splitting. The way I see it, it is the effect on a cavity's transmission spectrum of an atom (or quantum dot) inside the cavity. Well, this leads to two questions: 1) why is the cavity's transmission spectrum a "Lorenztian" bell, or something of the sort? 2)Why does the quantum dot have only one discrete absorption peak? It is made out of a solid (semicond.), so it must have a band structure, and thus a continuous spectrum for energies above the energy band width. So why is it discrete? Why is it only one sharp line? Thanks.