Degenerate Bose gas without anomalous averages

31st International Conference on Equations of State for Matter

Bobrov, V.B.^1,2 ; Trigger, S.A.^1 ; Schram, P.P.^3

Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13 Bldg 2, Moscow

125412, Russia^1

National Research University, Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow

111250, Russia^2

Eindhoven University of Technology, P.O. Box 513, Eindhoven

5600 MB, Netherlands^3

关键词: Annihilation operators;    Canonical ensemble;    Density of particles;    Density operators;    Dynamic structure factors;    Measurements of;    Single particle;    Zero-momentum;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/774/1/012149/pdf
DOI  :  10.1088/1742-6596/774/1/012149

来源: IOP

【 摘 要 】

Theory of a weakly non-ideal Bose gas in the canonical ensemble is developed without assumption of the C-number representation of the creation and annihilation operators with zero momentum. Instead of this assumption, we use the assumption on the C-number nature of the density operator N0= a†0a0with zero momentum. It is shown that the pole of the "density-density" Green function (DDGF), as well as the pole of the single-particle Green function (SPGF), exactly coincide with the Bogoliubov phonon-roton spectrum of excitations for both assumptions. This spectrum, as is known confirmed by many neutron and x-ray experimental measurements of the dynamic structure factor in He II, is straightly related to the DDGF. At the same time, we show that in the other case under consideration, when neither N0nor a†0and a0are C-numbers, a gap can exist in SPGF. This gap in SPGF excitations is straightly related to the density of particles in the "condensate". Therefore, the spectra of excitations for the DDGF and SPGF in the last case under consideration are different, in contrast to the Bogoliubov-type theory where these spectra are identical.