On the ground state energy of the inhomogeneous Bose gas

TL;DR

This paper derives an explicit, functional form for the ground state energy of an inhomogeneous Bose gas within the Hartree-Fock approximation, avoiding anomalous averages and applicable to strong interactions.

Contribution

It provides a new explicit energy functional for inhomogeneous Bose gases that extends beyond the Gross-Pitaevskii approach and is valid for strong interactions.

Findings

Explicit energy functional derived for inhomogeneous Bose gas

Kinetic energy form differs from Gross-Pitaevskii and is more general

Applicable to systems with strong interparticle interactions

Abstract

Within the self-consistent Hartree-Fock approximation, an explicit expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose-Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose-Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross-Pitaevski approach, is found. This form is valid beyond the Hartree-Fock approximation and can be applied for arbitrary strong interparticle interaction.