论文标题
对1D中量子三体问题的结合状态的软数字分析
Soft isogeometric analysis of the Bound States of a Quantum Three-Body Problem in 1D
论文作者
论文摘要
量子三体问题的研究集中在依赖准确数值近似的低能状态下。最近，采用了等几何分析（IGA）来解决该问题作为一种替代性但更强大的（相对于原子质量比）方法，该方法的表现优于经典的Born-oppenheimer（BO）近似。在本文中，我们专注于IGA的性能，并应用最近开发的软体模具以减少低能量结合状态的光谱误差。主要思想是在IgA双线性形式中添加带有惩罚参数的高级导数跳跃项。通过最佳的惩罚参数选择，我们观察到特征值误差超股份。我们专注于线性（有限元素）和二次元素，并通过多种示例（包括1D的两体和三体问题）在IgA上表现出比IgA的表现优于IgA的表现。
The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust (with respect to atom mass ratios) method that outperforms the classical Born-Oppenheimer (BO) approximation. In this paper, we focus on the performance of IGA and apply the recently-developed softIGA to reduce the spectral errors of the low-energy bound states. The main idea is to add high-order derivative-jump terms with a penalty parameter to the IGA bilinear forms. With an optimal choice of the penalty parameter, we observe eigenvalue error superconvergence. We focus on linear (finite elements) and quadratic elements and demonstrate the outperformance of softIGA over IGA through a variety of examples including both two- and three-body problems in 1D.
