一个高效求解含时Gross-Pitaevskii方程的算法  

An efficient algorithm for solving time-dependent Gross-Pitaevski equation

作　　者：舒丽莎 董光炯 SHU Lisha;DONG Guangjiong(State Key Laboratory of Precision Spectroscopy,East China Normal University,Shanghai200241,China)

机构地区：[1]华东师范大学精密光谱科学与技术国家重点实验室,上海200241

出　　处：《华东师范大学学报（自然科学版）》2024年第3期84-90,共7页Journal of East China Normal University(Natural Science)

摘　　要：Gross-Pitaevskii方程广泛应用于玻色-爱因斯坦凝聚体(Bose-Einstein condensate,BEC)的动力学研究,然而这个方程通常很难解析求解.因此发展相应的高精度数值求解方法非常重要.发展了结合算符劈裂法、Crank-Nicolson算法和四阶精度Numerov算法的高效求解Gross-Pitaevskii方程的新数值计算方法.通过数值计算可以表明,与传统的四阶精度的五点差分法相比,所提出的算法具有高效和消耗内存小的优点.The Gross-Pitaevskii equation is widely applied in Bose-Einstein condensate research,yet is rarely analytically determined;thus,it is important to develop a numerical method with high precision to resolve this.Accordingly,a numerical method was developed in this work,considering the splitting step method,Crank-Nicolson algorithm,and Numerov algorithm with four-order accuracy.The corresponding test shows that compared with the finite difference method using five points,the proposed algorithm is more efficient and costs less memory.

关 键 词：GROSS-PITAEVSKII方程 算符劈裂法 Crank-Nicolson算法 Numerov算法 

分 类 号：O411.3[理学—理论物理]