华东师范大学学报（自然科学版） ›› 2024, Vol. 2024 ›› Issue (3): 84-90.doi: 10.3969/j.issn.1000-5641.2024.03.009

• 原子、分子和光物理 • 上一篇    下一篇

一个高效求解含时Gross-Pitaevskii方程的算法

舒丽莎, 董光炯*()   

  1. 华东师范大学 精密光谱科学与技术国家重点实验室, 上海　200241
  • 收稿日期:2023-05-09 出版日期:2024-05-25 发布日期:2024-05-25
  • 通讯作者: 董光炯 E-mail:gjdong@phy.ecnu.edu.cn

An efficient algorithm for solving time-dependent Gross-Pitaevskii equation

Lisha SHU, Guangjiong DONG*()   

  1. State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai　200241, China
  • Received:2023-05-09 Online:2024-05-25 Published:2024-05-25
  • Contact: Guangjiong DONG E-mail:gjdong@phy.ecnu.edu.cn

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摘要：

Gross-Pitaevskii方程广泛应用于玻色-爱因斯坦凝聚体(Bose-Einstein condensate, BEC)的动力学研究, 然而这个方程通常很难解析求解. 因此发展相应的高精度数值求解方法非常重要. 发展了结合算符劈裂法、Crank-Nicolson算法和四阶精度Numerov算法的高效求解Gross-Pitaevskii方程的新数值计算方法. 通过数值计算可以表明, 与传统的四阶精度的五点差分法相比, 所提出的算法具有高效和消耗内存小的优点.

关键词: Gross-Pitaevskii方程, 算符劈裂法, Crank-Nicolson算法, Numerov算法

Abstract:

The Gross-Pitaevskii equation is widely applied in Bose-Einstein condensate research, yet is rarely analytically determined; thus, it is important to develop a numerical method with high precision to resolve this. Accordingly, a numerical method was developed in this work, considering the splitting step method, Crank-Nicolson algorithm, and Numerov algorithm with four-order accuracy. The corresponding test shows that compared with the finite difference method using five points, the proposed algorithm is more efficient and costs less memory.

Key words: Gross-Pitaevskii equation, splitting step method, Crank-Nicolson algorithm, Numerov algorithm

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