Influence of Omitting the P2 Term in the Multipole Photon-Matter Hamiltonian on the Stability and Propagation
The second order phase transition in the Dicke system in the state of thermal equilibrium, the so-called superradiant phase transition (SPT), has been studied by many authors since the work by Hepp and Lieb . In the Dicke system it is assumed that many two-level atoms interact with one another only through the transverse radiation field (the Maxwell field). In the mathematical formulation for SPT, either the truncated hamiltonian without the A2 term in the Coulomb-gauge-vector-potential formulation (type-I) [e.g., 1], or the one without the P2 term in the multipole hamiltonian formulation (type-II) [e.g., 2,3] has been used.
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