Legendre配置谱方法求解Bose-Einstein凝聚态的基态解  

The Legendre Collocation Spectral Method for the GroundState Solutions of the Bose⁃Einstein Condensates

作　　者：刘文杰 王汉权[1,2] LIU Wenjie;WANG Hanquan(School of Mathematics and Statistics,Yunnan University of Finance and Economics,Kunming 650221,P.R.China;School of Mathematics,Yunnan Normal University,Kunming 650504,P.R.China)

机构地区：[1]云南财经大学统计与数学学院,昆明650221 [2]云南师范大学数学学院,昆明650504

出　　处：《应用数学和力学》2023年第6期719-730,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11871418;11971120);云南基础研究计划重点项目(202101AS070044);云南省教育厅科研基金项目(2022Y547)。

摘　　要：近年来,有关Bose-Einstein凝聚态基态解的实验研究已经取得了一系列重要的成果.该文在相关研究成果的基础上,首先通过降维和无量纲化方法将Bose-Einstein凝聚态基态解问题转换成能量泛函极值问题,在离散该泛函时,尝试使用Legendre配置谱方法离散该能量泛函的一维和二维情形.其次,对该能量泛函极小值问题进行了数值模拟.最后,通过分析实验数据结果和图像得出,针对非旋转的Bose-Einstein凝聚态的基态解问题可以使用Legendre配置谱方法来求解,且数值结果的误差较小.In recent years,a series of important achievements have been made in the experimental study of the ground state solutions of the Bose Einstein condensates.First,the ground state solution problem of the Bose Einstein condensate was converted into the extreme value problem of energy functional with the dimensionless method.In the discretization of the energy functional,the Legendre collocation spectral method was used in the 1D and 2D cases.Second,the energy functional minimum problem was numerically simulated.The analyses of the experimental data and graphs show that,the Legendre collocation spectral method is applicable to the ground state solution of the non⁃rotating Bose Einstein condensate,and the errors of the numerical results are very small.

关 键 词：Bose-Einstein凝聚态 Legendre配置谱方法 数值计算 

分 类 号：O242[理学—计算数学]