旋转的双原子–玻色爱因斯坦凝聚体基态数值模拟
Numerical Simulations on Ground States for Rotating Two-Component Bose-Einstein Condensates
摘要: 静态相耦合的Gross-Pitaevskii方程组的解描述了双原子的玻色爱因斯坦凝聚体在极低温度下的基态现象。我们提出一种十分有效的数值方法——梯度法来求解此基态解。我们提出的梯度法在数值上既保持总模量守恒又能使总能量递减；我们严格地证明我们提出的梯度法是一种获得能量函数在给定限制性条件下的最小值(也即基态解)的十分有效的方法。我们通过大量的例子来显示该方法的优点并且应用该方法去研究处于旋转状态下的双原子–玻色爱因斯坦凝聚体在极低温度下所呈现的复杂涡旋现象。
Abstract: The ground states of rotating two-component Bose-Einstein condensates (BEC) at extremely low temperature are solutions of time-independent coupled Gross-Pitaevskii equations. To compute the ground states, we propose an efficient numerical method—gradient flows with discrete nor-malization. In linear cases and under properly chosen initial data, we can prove that the gradient flows converge into the ground state which has the lowest energy. We show that the method is quite efficient and apply the method to study complicated vortex structure in the ground state solutions of rotating two-component BEC at extremely low temperature.
文章引用：刘荣华, 邓云丹, 庞春平, 王汉权. 旋转的双原子–玻色爱因斯坦凝聚体基态数值模拟[J]. 应用数学进展, 2017, 6(9): 1187-1200. https://doi.org/10.12677/AAM.2017.69144

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