论文标题
动态发电机坐标方法中集体子空间的结构分析
Structural analysis of a collective subspace in the dynamical generator coordinate method
论文作者
论文摘要
在核理论中，一种形式混合方法的发电机坐标方法（GCM）通常用于集体运动的微观描述。但是，GCM存在一个问题，即集体子空间的结构（即由配置跨越的希尔伯特空间）尚不清楚。在本文中，我研究了动态GCM（DGCM）中集体子空间的结构，GCM的改进版本是GCM的改进版本。然后，我证明它仅限于在合理条件下结合张量产品和直接总和的特定形式。通过在实际数值计算中施加其他特定条件，可以将集体子空间作为集体零件的简单张量产物和其他条件写入。这些讨论不取决于用于生成配置的功能空间的细节，并且可以应用于各种方法，包括平均场理论。此外，该分析技术也可以应用于投影方法后的变体（VAP），然后揭示在特定条件下，VAP的功能空间具有无扭曲的结构。这些后果可以为与DGCM或GCM讨论集体动议提供强大的工具。
In nuclear theory, the generator coordinate method (GCM), a type of configuration mixing method, is often used for the microscopic description of collective motions. However, the GCM has a problem that a structure of the collective subspace, which is the Hilbert space spanned by the configurations, is not generally understood. In this paper, I investigate the structure of the collective subspace in the dynamical GCM (DGCM), an improved version of the GCM. I then show that it is restricted to a specific form that combines tensor products and direct sums under reasonable conditions. By imposing additional specific conditions that are feasible in actual numerical calculations, it is possible to write the collective subspace as a simple tensor product of the collective part and the others. These discussions are not dependent on the details of the function space used for generating the configurations and can be applied to various methods, including the mean-field theory. Moreover, this analytical technique can also be applied to a variation after projection method (VAP), then which reveals that under a specific condition, the function space of the VAP has an untwisted structure. These consequences can provide powerful tools for discussing the collective motions with the DGCM or the GCM.
