arXiv:cond-mat/0408023 · Europhysics Letters (EPL)

Ground-state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

Christoph Weiß, André Eckardt

Published Sep 22, 2004• 2 citations

Abstract

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason ( Phys. Rev. Lett. 80 (1998) 2504) have proved rigorously that the commonly accepted leading-order term of the ground-state energy is correct in the zero-density limit. Here, strong indications are given that also the next-to-leading term is correct. It is shown that the first terms obtained in a perturbative treatment provide contributions which are lost in the Bogoliubov approach.

DOI: 10.1209/epl/i2004-10169-6

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arXiv:cond-mat/0408023 · Europhysics Letters (EPL)

Ground-state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

Christoph Weiß, André Eckardt

Published Sep 22, 2004• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1209/epl/i2004-10169-6

Related papers

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Abstract For a translation invariant system of N bosons in the Gross–Pitaevskii regime, we establish a precise bound for the ground state energy

E_N

E N . While the leading, order N , contribution to

E_N

E N has been known since (Lieb et al. in Phys Rev A 61:043602, 2000; Lieb and Yngvason in Phys Rev Lett 80:2504–2507, 1998) and the second order corrections (of order one) have been first determined in Boccato et al. (Acta Math 222(2):219–335, 2019), our estimate also resolves the next term in the asymptotic expansion of

E_N

E N , which is of the order

(\log N) / N

( log N ) / N .

{{r}_{s}}^{\frac{3}{4}}

. The ground-state energy reduces to that calculated correctly by Brueckner, and earlier by Lee and Feenberg in a variational treatment. The excitation spectrum agrees with that calculated in our preceding paper using an entirely different method.

f=1.

The renormalized coupling constants are calculated and expressed in terms of the bare ones using the standard second-order perturbation method. With these renormalized coupling constants, we show that the ultraviolet divergence of the ground-state energy can be exactly eliminated.