Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction
Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction
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DOI：
10.4208/eajam.190310.170510a
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发表时间：
2011-02
影响因子：
1.2
通讯作者：
W. Bao;Yongyong Cai
中科院分区：
文献类型：
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作者：
W. Bao;Yongyong Cai
本文证明了描述具有内原子Josephson结的两组分Bose-Einstein凝聚体的耦合Gross-Pitaevskii方程基态解的存在唯一性，并得到了大参数下基态的极限解.本文提出了基于连续归一化梯度流和离散归一化梯度流的基态数值计算方法。提出了一种改进的后向欧拉有限差分格式来离散梯度流。数值结果证明了数值方法的有效性和准确性，并显示了问题中地面状态的丰富现象。
In this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting be- havior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the nu- merical methods and show the rich phenomena of the ground sates in the problem.