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

TL;DR

This paper models a degenerated weakly non-ideal Bose gas without using C-number representation, revealing that collective excitations follow Bogolyubov's spectrum while one-particle excitations have a density-dependent energy gap.

Contribution

It introduces a novel approach to modeling Bose gas without C-number representation, showing the coexistence of Bogolyubov spectrum and a density-dependent energy gap.

Findings

Collective excitations follow Bogolyubov's phonon-roton spectrum.

The one-particle excitation spectrum has a density-dependent energy gap.

The approach avoids the traditional C-number representation of zero-momentum operators.

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.