In this paper, we study the homogeneous one-dimensional bosonic gas interacting via a repulsive contact potential by using the improved Gaussian approximation. We obtain the gapless excitation spectrum of the Bogoliubov mode. Our result is in good agreement with the exact numerical calculation based on the Bethe ansatz. We speculate that the improved Gaussian approximation could be a quantitatively good approximation for higher-dimensional systems.

arXiv:1202.5355Physical Review AMar 6, 20123 citations

Communications in Mathematical Physics

On the asymptotic exactness of the Bogoliubov approximation for many boson systems

J. Ginibre

Published Mar 1, 1968• 141 citations

Publisher

DOI: 10.1007/bf01646422

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arXiv:1202.5355Physical Review AMar 6, 20123 citations

F

the strength parameter of the interaction). The factor $\ensuremath{\alpha}$ is found to be small and constant over a wide range of

F

and in this range the deviation of

W

from the Bogoliubov value is small. There is, however, a transition point

{F}_{T}

, beyond which $\ensuremath{\alpha}$ is constant and large and the usual Bogoliubov approximation is invalid for interactions more attractive than that characterized by

{F}_{T}

. A Bogoliubov-like approximation is shown to be quite accurate in this region. It is then shown that $F_{T}^{\ensuremath{-}1}$ is a linear function of the number of particles in the system.