Ground-State Energy of a Weakly Interacting Bose Gas: Calculation Without Regularization

Weiß, Christoph; Block, M. M.; Boers, Dave; Eckardt, André; Holthaus, Martin

doi:10.1515/zna-2004-1-201

Cited by 7 publications

(15 citation statements)

References 1 publication

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“…(19) and (20) numerically. It is convenient to measure the temperature T in units of ρΦ 0 and to treat n k and σ k as the functions of the dimensionless variable…”

Section: Normal and Anomalous Averagesmentioning

confidence: 99%

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Normal and anomalous averages for systems with Bose-Einstein condensate

Yukalov

Yukalova

2005

Laser Phys. Lett.

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The comparative behaviour of normal and anomalous averages as functions of momentum or energy, at different temperatures, is analysed for systems with Bose-Einstein condensate. Three qualitatively distinct temperature regions are revealed: The critical region, where the absolute value of the anomalous average, for the main energy range, is much smaller than the normal average. The region of intermediate temperatures, where the absolute values of the anomalous and normal averages are of the same order. And the region of low temperatures, where the absolute value of the anomalous average, for practically all energies, becomes much larger than the normal average. This shows the importance of the anomalous averages for the intermediate and, especially, for low temperatures, where these anomalous averages cannot be neglected. The anomalous value A(E) (solid line) and the normal average n(E) (dashed line) as functions of E for the reduced temperature T /ρΦ 0 = 1.5

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“…(19) and (20) numerically. It is convenient to measure the temperature T in units of ρΦ 0 and to treat n k and σ k as the functions of the dimensionless variable…”

Section: Normal and Anomalous Averagesmentioning

confidence: 99%

“…The diagonal Hamiltonian (12) makes it possible to find explicit expressions for different averages [20][21][22]. Our concern here is the normal average…”

Section: Normal and Anomalous Averagesmentioning

confidence: 99%

Normal and anomalous averages for systems with Bose-Einstein condensate

Yukalov

Yukalova

2005

Laser Phys. Lett.

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“…Here we follow an approach recently developed in Ref. [39], and employ a density expansion for computing the sum in the low-density limit: Starting from Eq. ( 64) with the abbreviations (15), somewhat tedious but straightforward calculations yield…”

Section: Ground-state Energy and Depletionmentioning

confidence: 99%

“…remains finite [39]. For evaluating these integrals, we introduce a dimensionless momentum variable x by demanding…”

Section: Ground-state Energy and Depletionmentioning

confidence: 99%

“…In order to obtain the ground-state energy of the system, the sum over all these shifts has to be evaluated; this is achieved in Sec. IV with the help of a density expansion which yields only finite quantities at each intermediate step of the calculation [39]. The depletions for a binary condensate are determined by the coefficients of the quasiparticle transformation, and calculated at the end of Sec.…”

Section: Introductionmentioning

confidence: 99%

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Ground-state energy and depletions for a dilute binary Bose gas

Eckardt¹,

Weiß²,

Holthaus³

2004

Phys. Rev. A

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When calculating the ground-state energy of a weakly interacting Bose gas with the help of the customary contact pseudopotential, one meets an artifical ultraviolet divergence which is caused by the incorrect treatment of the true interparticle interactions at small distances. We argue that this problem can be avoided by retaining the actual, momentum-dependent interaction matrix elements, and use this insight for computing both the ground-state energy and the depletions of a binary Bose gas mixture. Even when considering the experimentally relevant case of equal masses of both species, the resulting expressions are quite involved, and no straightforward generalizations of the known single-species formulas. On the other hand, we demonstrate in detail how these latter formulas are recovered from our two-species results in the limit of vanishing interspecies interaction.Comment: 11 pages, Phys. Rev. A in pres

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Self-consistent description of Bose–Bose droplets: modified gapless Hartree–Fock–Bogoliubov method

Ziń

Pylak²,

Idziaszek³

et al. 2022

New J. Phys.

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We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the Generalized Gross -- Pitaevskii equation accounting for quantum depletion and renormalized anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations. We derive well defined procedure to calculate the zero temperature renormalized anomalous density - the quantity needed to correctly describe the formation of quantum liquid droplet. We pay particular attention to the case of droplets harmonically confined in some directions. The method allows to determine the Lee-Huang-Yang-type contribution to the chemical potential of inhomogeneous droplets when the local density approximation fails.

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Ground-State Energy of a Weakly Interacting Bose Gas: Calculation Without Regularization

Cited by 7 publications

References 1 publication

Normal and anomalous averages for systems with Bose-Einstein condensate

Normal and anomalous averages for systems with Bose-Einstein condensate

Ground-state energy and depletions for a dilute binary Bose gas

Self-consistent description of Bose–Bose droplets: modified gapless Hartree–Fock–Bogoliubov method

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