Coexistence of the "bogolons" and the one-particle spectrum of excitations with a gap in the degenerated Bose gas

TL;DR

This paper investigates the properties of a weakly non-ideal Bose gas, revealing that it exhibits both gapped one-particle excitations and phonon-roton collective excitations, with a focus on their coexistence.

Contribution

It demonstrates the coexistence of gapped one-particle excitations and Bogolyubov-like collective excitations in a degenerated Bose gas without using C-number representation.

Findings

The one-particle excitation spectrum has a gap related to condensate density.

The density-density Green function shows a phonon-roton spectrum identical to Bogolyubov's.

Both types of excitations coexist in the weakly non-ideal Bose gas.

Abstract

Properties of the weakly non-ideal Bose gas are 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 of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-roton spectrum of excitations which exactly coincides with one discovered by Bogolyubov for the collective excitations (the "bogolons").