A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates

Authors:
Weizhu Bao;Jie Shen
Affiliations:
Department of Mathematics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117543, Singapore;Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A generalized-Laguerre-Hermite pseudospectral method is proposed for computing symmetric and central vortex states in Bose-Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The new method is based on the properly scaled generalized-Laguerre-Hermite functions and a normalized gradient flow. It enjoys three important advantages: (i) it reduces a three-dimensional (3D) problem with cylindrical symmetry into an effective two-dimensional (2D) problem; (ii) it solves the problem in the whole space instead of in a truncated artificial computational domain and (iii) it is spectrally accurate. Extensive numerical results for computing symmetric and central vortex states in BECs are presented for one-dimensional (1D) BEC, 2D BEC with radial symmetry and 3D BEC with cylindrical symmetry.