计算自旋轨道耦合 Spin-2 BEC 基态的带拉格朗日乘子的正规梯度流法

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1607-1619.

计算自旋轨道耦合 Spin-2 BEC 基态的带拉格朗日乘子的正规梯度流法

袁永军()

计算与随机数学教育部重点实验室 & 湖南师范大学数学与统计学院长沙 410081

收稿日期:2022-08-26 修回日期:2023-03-23 出版日期:2023-10-26 发布日期:2023-08-09
作者简介:袁永军，Email: yyj1983@hunnu.edu.cn
基金资助:
国家自然科学基金(11971007)

A Normalized Gradient Flow with Lagrange Multipliers for Computing Ground States of Spin-Orbit Coupled Spin-2 Bose-Einstein Condensates

Yuan Yongjun()

LCSM (MOE) & School of Mathematics and Statistics, Hunan Normal University, Changsha 410081

Received:2022-08-26 Revised:2023-03-23 Online:2023-10-26 Published:2023-08-09
Supported by:
NSFC(11971007)

摘要/Abstract

摘要：

该文设计带拉格朗日乘子的正规梯度流法 (GFLM) 模拟自旋轨道耦合 Spin-2 玻色-爱因斯坦凝聚 (BEC) 的基态. 发掘投影系数间的隐含关系, 解决了模型中已有条件 (总质量及总磁场量守恒) 不足以确定所有投影系数的困难. 对循环型/铁磁体系下具有不同势函数的自旋轨道耦合 Spin-2 BEC 的基态进行了大量数值试验, 验证了算法的有效性, 并揭示了自旋轨道耦合 Spin-2 BEC 的条纹状基态与晶格状基态随自旋轨道耦合系数相互转化的相变规律.

关键词: 玻色-爱因斯坦凝聚, 基态, 正规梯度流法, 拉格朗日乘子

Abstract:

In this paper, a normalized gradient flow with Lagrange multipliers is designed to compute ground states of spin-orbit coupled Spin-2 Bose-Einstein condensates. By excavating the implicit relation between projection coefficients, the difficult that the existed conditions (the conservation of total mass and magnetization) of the model problem is insufficient to determine all the projection coefficients, is overcome. Extensive numerical experiments are done to compute the ground states of spin-orbit coupled Spin-2 BECs with cyclic/ferromagenetic interactions. As a result, the effectiveness of the two algorithms is verified, and the phase transformation law about how the stripe pattern ground states and the square-lattice pattern ground states of spin-orbit coupled Spin-2 BECs change to each other with the spin-orbit coupling parameter,are revealed.

Key words: Bose-Einstein condensate, Ground state, Normalized gradient flow, Lagrange multiplier

中图分类号:

O242.1

袁永军. 计算自旋轨道耦合 Spin-2 BEC 基态的带拉格朗日乘子的正规梯度流法[J]. 数学物理学报, 2023, 43(5): 1607-1619.

Yuan Yongjun. A Normalized Gradient Flow with Lagrange Multipliers for Computing Ground States of Spin-Orbit Coupled Spin-2 Bose-Einstein Condensates[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1607-1619.

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