摘要
针对分数阶玻色-爱因斯坦凝聚态(BEC)的基态和第一激发态进行了研究。首先使用归一化梯度流的方法将分数阶玻色-爱因斯坦凝聚态的基态问题转化为求解分数阶Gross-Pitaevskii方程的最小能量问题。由于分数阶拉普拉斯算子的非局部性质,计算分数阶GP方程的特征值和特征函数是一个挑战。传统的Grünwald-Letnikov差分法精度低、稳定性差。利用加权偏移的Grünwald-Letnikov差分法(WSGD)进行空间离散,离散结果为一个常微分方程组,具有二阶精度并且无条件稳定。时间离散方面采用了隐式积分因子(IIF)方法,计算精度高、存储量小、效率高。最后,数值实验通过调节分数阶阶数α和非线性参量β来演示包含谐振子势的BEC的基态和第一激发态。数值结果表明了2种数值方法的收敛性、高效性和准确性。
In this paper,numerical methods of the ground and first excited states of the fractional Bose-Einstein condensates(BEC)have been conducted.First,we use the normalized gradient flow scheme to calculate the minimum energy problem of Gross-Pitaevskii equation.Because of the nonlocality of the fractional Laplace operator,it is a challenge to calculate the eigenvalues and eigenfunctions of the fractional GP equation.The traditional Grünwald-Letnikov difference method has low precision and poor stability.Weighted and shifted Grünwald-Letnikov difference method is used for space discretization.The discrete result is a system of ordinary differential equations,and unconditionally stable with two order precision.For the time discretization,we adopt implicit integration factor(IIF)method,which has the adventages of high calculation accuracy,small storage capacity and efficient.Finally,numerical experiments demonstrate the ground state and the first excited state of BEC with harmonic oscillator potential by altering the fractional orderand nonlinear parameters.Numerical results show the convergence,efficiency and accuracy of the above potential wells.
作者
邵永运
韩子健
张荣培
王语
SHAO Yongyun;HAN Zijian;ZHANG Rongpei;WANG Yu(Discipline and Scientific Research Office,Shenyang Normal University,Shenyang 110034,China;College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)
出处
《沈阳师范大学学报（自然科学版）》
CAS
2018年第5期417-423,共7页
Journal of Shenyang Normal University:Natural Science Edition
基金
辽宁省科技厅自然科学基金资助项目(2014020121)
