Chin. Phys. Lett.  2017, Vol. 34 Issue (6): 060202    DOI: 10.1088/0256-307X/34/6/060202
A High-Order Conservative Numerical Method for Gross–Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC
Xiang Li1, Xu Qian1,2**, Ling-Yan Tang1, Song-He Song1
1College of Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073
2Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410073
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Xiang Li, Xu Qian, Ling-Yan Tang et al  2017 Chin. Phys. Lett. 34 060202
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Abstract We propose a high-order conservative method for the nonlinear Schrödinger/Gross–Pitaevskii equation with time-varying coefficients in modeling Bose–Einstein condensation (BEC). This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
Received: 05 January 2017      Published: 23 May 2017
PACS:  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.70.Bf (Finite-difference methods)  
  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Jh (Numerical differentiation and integration)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570, the Open Foundation of State Key Laboratory of High Performance Computing of China, the Research Fund of National University of Defense Technology under Grant No JC15-02-02, and the Fund from HPCL.
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Xiang Li
Xu Qian
Ling-Yan Tang
Song-He Song
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