Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases

TL;DR

This paper presents a self-consistent, gapless Hartree-Fock-Bogoliubov approximation for dilute Bose gases with Bose-Einstein condensate, ensuring physical normalization conditions are satisfied.

Contribution

It introduces a method to make the Hartree-Fock-Bogoliubov approximation both conserving and gapless by incorporating all relevant normalization conditions.

Findings

The approximation is both conserving and gapless.

Normalization conditions are crucial for self-consistency.

The approach is applicable to dilute Bose-Einstein condensates.

Abstract

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.