论文标题
散射问题的奇异价值分解的最小二乘方法
Least-square approach for singular value decompositions of scattering problems
论文作者
论文摘要
最近观察到，可以使用基质分解技术（例如奇异值分解）有效地表示手性的两体相互作用。但是，在几个或多体框架中对这些低级结构的剥削是不平凡的，需要明确利用分解格式的重新进行。在这项工作中，我们提出了一种一般最小二乘方法，该方法适用于不同的少数和多体框架，并可以在最小二乘迭代中有效地减少到较少的单数值。我们通过以分解形式求解Lippmann-Schwinger方程来验证最小二乘方法的可行性。发现$ t $矩阵的最终低级别近似值可完全捕获散射观测值。讨论了最小二乘方法在其他框架上的潜在应用，以采用张量分解技术。
It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or many-body framework is nontrivial and requires reformulations that explicitly utilize the decomposition format. In this work, we present a general least-square approach that is applicable to different few- and many-body frameworks and allows for an efficient reduction to a low number of singular values in the least-square iteration. We verify the feasibility of the least-square approach by solving the Lippmann-Schwinger equation in factorized form. The resulting low-rank approximations of the $T$ matrix are found to fully capture scattering observables. Potential applications of the least-square approach to other frameworks with the goal of employing tensor factorization techniques are discussed.
