A GENERALIZED-LAGUERRE-FOURIER-HERMITE PSEUDOSPECTRAL METHOD FOR COMPUTING THE DYNAMICS OF ROTATING BOSE-EINSTEIN CONDENSATES

被引：69
作者：
Bao, Weizhu [1 ,2 ]
Li, Hailiang [3 ]
Shen, Jie [4 ]
机构：
[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore
[2] Natl Univ Singapore, Ctr Computat Sci & Engn, Singapore 117543, Singapore
[3] Capital Normal Univ, Sch Math, Beijing 100037, Peoples R China
[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2009年 / 31卷 / 05期
关键词：
generalized-Laguerre-Fourier-Hermite functions; rotating Bose-Einstein condensate; angular momentum rotation; time-splitting; energy; condensate width; GROSS-PITAEVSKII EQUATION; CENTRAL VORTEX STATES; SPECTRAL METHODS; DIFFERENTIAL-EQUATIONS; EFFICIENT COMPUTATION; UNBOUNDED-DOMAINS; STABILITY; TRAPS; GASES;
D O I：
10.1137/080739811
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A time-splitting generalized-Laguerre-Fourier-Hermite pseudospectral method is proposed for computing the dynamics of rotating Bose-Einstein condensates (BECs) in two and three dimensions. The new numerical method is based on the following: (i) the use of a times-plitting technique for decoupling the nonlinearity; (ii) the adoption of polar coordinates in two dimensions and cylindrical coordinates in three dimensions such that the angular rotation term becomes constant coefficient; and (iii) the construction of eigenfunctions for the linear operator by properly scaling the generalized-Laguerre, Fourier, and Hermite functions. The new method enjoys the following properties: (i) it is explicit, time reversible, and time transverse invariant; (ii) it conserves the position density and is spectrally accurate in space and second-order or fourth-order accurate in time; and (iii) it solves the problem in the original whole space instead of in a truncated artificial computational domain. The method is also extended to solve the coupled Gross-Pitaevskii equations for the dynamics of rotating two-component and spin-1 BECs. Extensive numerical results for the dynamics of BECs are reported to demonstrate the accuracy and efficiency of the new method for rotating BECs.
引用
收藏
页码：3685 / 3711
页数：27
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