Bose-Einstein凝聚问题基态解的数值方法比较和分析  

Comparison and analysis of numerical methods for ground state solution of Bose-Einstein condensation

作　　者：曹蕊 华冬英[1] 王茜 张读翠 李祥贵[1] CAO Rui;HUA Dongying;WANG Xi;ZHANG Ducui;LI Xianggui(School of Applied Science,Beijing Information Science&Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2021年第6期6-13,68,共9页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金资助项目(11671044)。

摘　　要：使用有限差分方法求解描述玻色—爱因斯坦凝聚的Gross-Pitaevskii方程的基态解。首先使用虚时法将Gross-Pitaevskii方程转为能量耗散的方程,再通过投影法使能量耗散方程满足原方程中的归一化条件。其次,对归一化的耗散方程空间方向采用经典的二阶中心差分格式进行离散,时间方向分别使用向后欧拉格式和Crank-Nicolson格式进行完全离散。提出了一种迭代求解方法对所得非线性离散方程进行计算,与常规采用的线性化处理方法所得的数值结果进行详细的比较和分析。结果表明线性化求解法和迭代求解法这两种算法均可用于求解基态解,计算所得能量均随时间演化呈衰减趋势。The finite difference method was used to solve the ground state solution of the Gross-Pitaevskii equation describing the Bose–Einstein condensation.Firstly,the imaginary time method was used to transform the Gross-Pitaevskii equation into the energy dissipation equation,then the projection method was used to make the energy dissipation equation satisfy the normalization condition in the original equation.Secondly,the spatial direction of the normalized dissipative equation was discretized by the classical second-order central difference scheme,and the time direction was discretized by backward Euler finite difference scheme and Crank-Nicolson finite difference scheme respectively.In addition,an iterative method was proposed to calculate the nonlinear discrete equations,and the numerical results obtained by the direct linearization method were compared and analyzed in detail.The numerical results show that both the linearization method and the iterative method can be used to solve the ground state solution,and the energy of both methods decreases with time evolution.

关 键 词：玻色—爱因斯坦凝聚 基态解 虚时法 向后欧拉格式 Crank-Nicolson有限差分格式 

分 类 号：O241.82[理学—计算数学]