An evolution operator and the dynamics of model systems (Q1814564)

The paper deals with the non-equilibrium dynamics of the model hamiltonian of the Dicke type by using the method of functional integration. The free hamiltonian is the sum of the free hamiltonian for Bose systems plus the hamiltonian of Fermi operators corresponding to the two-level atoms. The perturbed hamiltonian contains an interaction between the ideal systems. It is assumed that the initial state of the system is an equilibrium state with respect to the hamiltonian without the interaction term and that its evolution is given by the hamiltonian with the interaction term. The evolution can be described either by the density matrix or by the temperature-temporal Green function. The expressions of these quantities in terms of the functional integrals are given. The Dyson equation for the two-time Green function and the Schwinger equation are derived. They are shown to correspond, for the studied system, to the elimination of the Bose variables method due to N. N. Bogoliubov and N. N. Bogoliubov Jr.