Please use this identifier to cite or link to this item: https://doi.org/10.1137/070698488
Title: Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow
Authors: Bao, W. 
Lim, F.Y.
Keywords: Backward-forward Euler sine-pseudospectral method
Coupled Gross-Pitaevskii equations
Ground state
Normalized gradient flow
Spin-1 Bose-Einstein condensate
Issue Date: 2007
Citation: Bao, W., Lim, F.Y. (2007). Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow. SIAM Journal on Scientific Computing 30 (4) : 1925-1948. ScholarBank@NUS Repository. https://doi.org/10.1137/070698488
Abstract: In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose-Einstein condensates (BECs) by using the normalized gradient flow or imaginary time method. The key idea is to find a third projection or normalization condition based on the relation between the chemical potentials so that the three projection parameters used in the projection step of the normalized gradient flow are uniquely determined by this condition as well as the other two physical conditions given by the conservation of total mass and total magnetization. This allows us to successfully extend the most popular and powerful normalized gradient flow or imaginary time method for computing the ground state of a single-component BEC to compute the ground state of spin-1 BECs. An efficient and accurate discretization scheme, the backward-forward Euler sine-pseudospectral method, is proposed to discretize the normalized gradient flow. Extensive numerical results on ground states of spin-1 BECs with ferromagnetic/antiferromagnetic interaction and harmonic/optical lattice potential in one/three dimensions are reported to demonstrate the efficiency of our new numerical method. © 2008 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Scientific Computing
URI: http://scholarbank.nus.edu.sg/handle/10635/103031
ISSN: 10648275
DOI: 10.1137/070698488
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