Hartree-Fock-Bogolubov method in the theory of Bose-condensed systems

TL;DR

This paper addresses the Hohenberg-Martin dilemma in Bose-condensed systems by proposing an approach within the Hartree-Fock-Bogolubov approximation that achieves a balance between conservation laws and a gapless spectrum, aligning well with experimental data.

Contribution

The paper introduces a method within the Hartree-Fock-Bogolubov framework that resolves the conservation-gap dilemma in Bose-Einstein condensate theories.

Findings

The approach provides a gapless spectrum while conserving physical laws.

Quantitative agreement with experimental data is achieved.

The method offers a stable description of Bose-condensed systems.

Abstract

The Hohenberg-Martin dilemma of conserving versus gapless theories for systems with Bose-Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose-Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservation laws, describing a stable system, but the spectrum acquires a gap, which means that the condensate cannot appear. An approach is described, resolving this dilemma, and it is shown to give good quantitative agreement with experimental data. Calculations are accomplished in the Hartree-Fock-Bogolubov approximation.