On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model

A system of N two-level molecules coupled to finitely many modes of a quantized radiation field via a truncated dipolar interaction is investigated. The thermodynamic and correlation functions can be exactly computed in the limit N → ∞. The system exhibits a second order phase transition from normal to superradiance. Different effective Hamiltonians with linear Heisenberg equations of motion become asymptotically exact in the limit N → ∞.