A canonical transformation theory of the generalised Dicke model

The Hamiltonian of the generalised Dicke model is transformed to describe collective excitations above a ground state. When the wavelength of the field modes is considerably less than the system dimensions the condition for the existence of a phase transition in a lattice configuration differs from the long-wave result. The effect of atomic separation on certain ground state properties is examined and a short description of the excitation spectrum is given. For a dielectric crystal it is shown that the super-radiant phase transition is impossible in principle for up to 48 modes.