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

作者：Bao Weizhu^*; Li Hailiang; Shen Jie

来源：SIAM Journal on Scientific Computing, 2009, 31(5): 3685-3711.

DOI：10.1137/080739811

• generalized-Laguerre-Fourier-Hermite functions
• rotating Bose-Einstein condensate
• angular momentum rotation
• time-splitting
• energy
• condensate width

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.

• 出版日期2009
• 单位首都师范大学