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Trapped Bose-Einstein Condensates: Role of Dimensionality

Yuri S. Kivshar·Tristram J. Alexander
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Abstract

We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1,2,3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external anisotropic parabolic potential. While for the positive scattering length the stationary ground-state solutions of the Gross-Pitaevskii equation are shown to be always stable independently of the spatial dimension, for the negative scattering length the ground-state condensate is stable only in the 1D and 2D cases, whereas in the 3D case it becomes unstable. A direct link between nonlinear modes of BECs and (bright and dark) solitary waves of the nonlinear Schrodinger equation is demonstrated for all the dimensions.

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Yuri S. Kivshar, Tristram J. Alexander. 1999-05-05. Trapped Bose-Einstein Condensates: Role of Dimensionality. https://arxiv.org/abs/cond-mat/9905048

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