Bose-Einstein凝聚态基态解的加权数值方法及稳定性分析  

Weighted numerical method and stability analysis for the groundstate solution of Bose-Einstein condensate

作　　者：吕思琪 廖翠萃 LÜSiqi;LIAO Cuicui(College of Science,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江南大学理学院,无锡214122

出　　处：《北京信息科技大学学报（自然科学版）》2024年第2期92-98,共7页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金项目(61973137,11401259);江苏省自然科学基金项目(BK20201339)。

摘　　要：构造加权法离散归一化梯度流,求解玻色-爱因斯坦凝聚态(Bose-Einstein condensate, BEC)的基态解,整合和扩充了离散归一化梯度流的经典有限差分法。同时,结合冯·诺伊曼(von Neumann)条件和冻结系数法证明了不同加权因子下数值格式的稳定性条件。从局部截断误差大小来看,加权法的最优加权因子为1/2。数值实验验证了加权法的稳定性条件,表明加权法可有效求解基态,且在求解过程中能量随时间演化呈递减趋势。另外,当加权因子取值为1/3时,数值结果展示对应数值格式在空间方向具有二阶收敛性。The ground state solution of Bose-Einstein condensate(BEC)was computed by constructing a weighted method to discrete normalized gradient flow,integrating and expanding classical finite difference methods for the discrete normalized gradient flow.Meanwhile,the stability conditions for the numerical scheme under different weighted factors were proved using the von Neumann condition and the frozen coefficient method.From the point of local truncation error,the optimal weighted factor of this weighted method is 1/2.Numerical experiments verified the stability conditions of the weighted method,showing that the weighted method can effectively solve the ground state,and the energy decreases during the time evolution process.In addition,when the weighted factor is taken as 1/3,numerical results show that the corresponding numerical scheme has second-order convergence in the spatial direction.

关 键 词：玻色-爱因斯坦凝聚态 基态解 加权法 稳定性 归一化梯度流 

分 类 号：O241.82[理学—计算数学]