A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates
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DOI：
10.1137/130911111
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发表时间：
2013-11
期刊：
SIAM J. Sci. Comput.
影响因子：
--
通讯作者：
W. Bao;Daniel Marahrens;Q. Tang;Yanzhi Zhang
W. Bao;Daniel Marahrens;Q. Tang;Yanzhi Zhang
中科院分区：
其他
文献类型：
--
作者：
W. Bao;Daniel Marahrens;Q. Tang;Yanzhi Zhang

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We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose--Einstein condensates (BECs) in a rotational frame with or without long-range dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the two-dimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dyn...