旋转的双原子–玻色爱因斯坦凝聚体基态数值模拟.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1187-1200 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69144 Numerical Simulations on Ground States for Rotating Two-Component Bose-Einstein Condensates Ronghua Liu, Yundan Deng, Chunping Pang, Hanquan Wang School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming Yunnan nd th th Received: Dec. 2 , 2017; accepted: Dec. 19 , 2017; published: Dec. 26 , 2017 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 so- lutions of rotating two-component BEC at extremely low temperature. Keywords Coupled Gross-Pitaevskii Equations, Rotating Two-Component Bose-Einstein Condensates, Gradient Flows 旋转的双原子–玻色爱因斯坦凝聚体基态 数值模拟 刘荣华，邓云丹，庞春平，王汉权 云南财经大学统计与数学学院，云南 昆明 收稿日期：2017年12月2 日；录用日期：2017年12月19 日；发布日期：2017年12月26 日 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 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. DOI: 10.12677/aam.2017.69144 刘荣华 等 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