NDLI: A Generalized-LaguerreFourierHermite Pseudospectral Method for Computing the Dynamics of Rotating BoseEinstein Condensates

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Shen, Jie Li, Hailiang Bao, Weizhu
Copyright Year	2009
Abstract	A time-splitting generalized-LaguerreFourierHermite pseudospectral method is proposed for computing the dynamics of rotating BoseEinstein condensates (BECs) in two and three dimensions. The new numerical method is based on the following: (i) the use of a time-splitting 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 GrossPitaevskii 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.
Starting Page	3685
Ending Page	3711
Page Count	27
File Format	PDF
ISSN	10648275
DOI	10.1137/080739811
e-ISSN	10957197
Issue Number	5
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-10-01
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods Computational methods time-splitting condensate width Spectral, collocation and related methods angular momentum rotation NLS-like equations generalized-LaguerreFourierHermite functions rotating BoseEinstein condensate energy Applications to physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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