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The theory of model Hamiltonians and the method of functional integration. (English. Russian original) Zbl 0728.58042
Proc. Steklov Inst. Math. 184, 117-145 (1991); translation from Tr. Mat. Inst. Steklova 184, 105-129 (1990).
The statistical mechanics of the Dicke-type models (describing the super- radiance) is studied using the path integral methods. The partition function is obtained (in the thermodynamic limit) above and below the critical temperature. The Green functions and the spectra of bosonic excitations are calculated. The corresponding results for the BCS model are presented.
The above results are obtained by dividing the integration domain in the path integral into two parts - the neighbourhood of the stationary phase points and the rest. The dominating contribution from the first region is calculated and the estimate for the remainder is given. The contribution coming from the second region can be also rigorously estimated.
58Z05 Applications of global analysis to the sciences
82B99 Equilibrium statistical mechanics
81S40 Path integrals in quantum mechanics