Collective excitations and the gap in spectrum of the degenerated Bose gas

V. B. Bobrov; S. A. Trigger

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arXiv · 0910.3455

Collective excitations and the gap in spectrum of the degenerated Bose gas

V. B. Bobrov·S. A. Trigger

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Abstract

Model of the degenerated weakly non-ideal Bose gas is considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function are calculated on basis of the suggestion about C-number representation of the operator of particle density in the Bose condensate. It is shown, that the pole in the "density-density" Green function determines the Bogolyubov's spectrum of the collective excitations, which have the phonon-roton form. At the same time the spectrum of the one-particle excitations possesses a gap, whose value is connected with the density of particles in the Bose condensate.

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V. B. Bobrov, S. A. Trigger. 2009-10-19. Collective excitations and the gap in spectrum of the degenerated Bose gas. https://arxiv.org/abs/0910.3455

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