An efficient numerical method for computing dynamics of spin F = 2 Bose–Einstein condensates

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• 作者：Hanquan Wang ; ^a ; ^b ; ^{hanquan.wang@gmail.com"" rel=""nofollow}
• 关键词：Gross– ; Pitaevskii equations ; Spin F = 2 BEC ; Time-splitting Fourier pseudospectral method ; Numerical simulation ; Quantized vortices
• 刊名：Journal of Computational Physics
• 出版年：2011
• 出版时间：1 July 2011
• 年：2011
• 卷：230
• 期：15
• 页码：6155-6168
• 全文大小：1920 K

文摘

In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross–Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose–Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose–Einstein condensates confined in a uniform/nonuniform magnetic field.