数值求解耦合Gross-Pitaevskii方程组基态解的离散归一化梯度流方法  

Numerical method for the ground state solution of coupled Gross-Pitaevskii equations

作　　者：赵子尧 马强 ZHAO Zi-Yao;MA Qiang(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,610064

出　　处：《四川大学学报（自然科学版）》2024年第1期9-14,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11801387);四川省自然科学基金(2022NSFSC0322)。

摘　　要：本文提出了一种求解磁场项为常数的耦合Gross-Pitaevskii方程组基态解的数值方法.基于单组分近似理论,本文将方程组的能量函数等价为单组分的能量泛函,然后基于降阶后的能量表达式提出了离散归一化梯度流数值方法.数值算例表明,该方法高效且可靠.In this paper,a numerical method for solving the ground state solution of the coupled Gross-Pitaevskii equations with constant magnetic field term is proposed.Based on the single mode approximation theory,energy function of the equations is equivalently expressed by a reduced energy function with single component.Then,based on the method of discrete normalized gradient flow,the method is proposed by using the expression of reduced energy function.Numerical examples illustrate the reliability and performance of the method.

关 键 词：耦合Gross-Pitaevskii方程组 基态解 单组分近似 归一化梯度流 

分 类 号：O241.8[理学—计算数学]