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Nuclear Physics A

Boson expansions and Hartree-Bogoliubov theory

Eugene R. Marshalek, G. Holzwarth

Published Aug 1, 1972• 35 citations
Publisher
DOI
10.1016/0375-9474(72)90526-x

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A possible quantization is proposed with respect to time-dependent Hartree-Bogoliubov theory based on the SO(2N+1) algebra which was presented by Fukutome, Nishiyama and the present author. The adopted quantization procedure is an extension of Marshalek and Holzwarth's idea used in the case of the conventional time-dependent Hartree-Bogoliubov theory based on the SO(2N) algebra. As a natural consequent of the quantization, Holstein-Primakoff type boson expansion theory can be derived in a unified form of even and odd particle system.
This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of N bosons with an interaction of intensity 1 / N (mean-field regime). In the limit N → ∞ , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these systems.