arXiv:cond-mat/0401112 · Physical Review A

Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

Shujuan Liu, Hongwei Xiong, Guoxiang Huang, Xu Zhi-Jun

Published Dec 30, 2003• 5 citations

Abstract

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{N}^{22/15}$ and the fluctuations vanish when temperature approaches the BEC critical temperature.

DOI: 10.1103/physreva.68.065601

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arXiv:cond-mat/0401112 · Physical Review A

Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

Shujuan Liu, Hongwei Xiong, Guoxiang Huang, Xu Zhi-Jun

Published Dec 30, 2003• 5 citations

arXiv HTML PDF

Abstract

〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{N}^{22/15}

and the fluctuations vanish when temperature approaches the BEC critical temperature.

DOI: 10.1103/physreva.68.065601

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〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{N}^{22/15}

and the fluctuations vanish when temperature approaches the BEC critical temperature.

{N}^{2},

where N is the total number of particles. For the quasi-2D BEC, the particle-number fluctuations are proportional not only to

{N}^{2}

but also to the square root of the trapping frequency in the strongly confined direction.

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume

V

follow the law $〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{V}^{4/3}$. This anomalous behavior arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.