The classical analogue of the superradiant phase transition in the Dicke model

We construct the classical analogue of the phenomenon of superradiance in the zero temperature limit and show that a simple geometrical interpretation can be given in the integrable case. The nonintegrable case is also studied and in both cases we find bifurcation of equilibrium for the same parameter values where this phase transition is known do occur in the Thermodynamical context. The ground state of the system is also studied in the framework of a mean field approximation and a simple analytical expression obtained. A connection between the classical and quantum points of view is presented. (author)