Trapped Bose-Einstein Condensates: Role of Dimensionality
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.
Cite
@article{arxiv.cond-mat/9905048,
title = {Trapped Bose-Einstein Condensates: Role of Dimensionality},
author = {Yuri S. Kivshar and Tristram J. Alexander},
journal= {arXiv preprint arXiv:cond-mat/9905048},
year = {2007}
}
Comments
11 pages, 10 figures To appear in the Proceeding of the APCTP-Nankai Symposium on Yang-Baxter Systems, Nonlinear Models and Their Applications. Eds. Q-Han Park et al. (World Scientific, Singapore, 1999) in press