Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow
Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow
复制标题
DOI：
10.1137/070698488
复制
发表时间：
2008-01-01
影响因子：
3.1
通讯作者：
Lim, Fong Yin
中科院分区：
文献类型：
--
作者：
Bao, Weizhu;Lim, Fong Yin
本文利用归一化梯度流或虚时间方法，提出了一种计算自旋为1的玻色-爱因斯坦凝聚（BEC）基态的有效而精确的数值方法。其关键思想是基于化学势之间的关系找到第三投影或归一化条件，使得在归一化梯度流的投影步骤中使用的三个投影参数由该条件以及由总质量守恒和总磁化强度守恒给出的另外两个物理条件唯一地确定。这使我们能够成功地扩展最流行的和强大的归一化梯度流或虚时方法计算基态的单组分BEC计算自旋1 BEC的基态。本文提出了一种高效、精确的离散格式--前后向欧拉正弦拟谱法。对自旋为1的BEC在铁磁/反铁磁相互作用和一维/三维简谐/光学晶格势作用下的基态进行了大量的数值计算，结果表明了我们新的数值方法的有效性.
In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose-Einstein condensates (BECs) by using the normalized gradient flow or imaginary time method. The key idea is to find a third projection or normalization condition based on the relation between the chemical potentials so that the three projection parameters used in the projection step of the normalized gradient flow are uniquely determined by this condition as well as the other two physical conditions given by the conservation of total mass and total magnetization. This allows us to successfully extend the most popular and powerful normalized gradient flow or imaginary time method for computing the ground state of a single-component BEC to compute the ground state of spin-1 BECs. An efficient and accurate discretization scheme, the backward-forward Euler sine-pseudospectral method, is proposed to discretize the normalized gradient flow. Extensive numerical results on ground states of spin-1 BECs with ferromagnetic/antiferromagnetic interaction and harmonic/optical lattice potential in one/three dimensions are reported to demonstrate the efficiency of our new numerical method.