发表机构
Indian Institute of Science Education and Research; MindBrug Research LLP（印度科学教育研究所; MindBrug研究有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出最佳子集技术，通过比较谱涨落与随机矩阵系综，无需去对称化即可确定厄米和非厄米复合量子谱中的对称扇区数量，并在高斯、Wishart、Ginibre及多体量子谱上验证。
AI 中文摘要
复杂量子系统中的谱涨落通常用随机矩阵谱来建模。只有当量子谱是纯序列，而非混合了不同对称扇区能级的复合谱时，才能与随机矩阵取得定量一致。先前研究表明，在对称扇区维度相等的情况下，可以利用高阶间距比统计量检测复合谱中的离散对称性。一般情形是对称扇区维度不等，且哈密顿系统的对称性未知或仅部分已知。在本工作中，我们探讨如何在厄米和非厄米背景下，从复合谱中确定对称扇区的数量。我们提出了一种最佳子集技术，通过将谱涨落与适当的随机矩阵系综进行比较来确定对称扇区数量，而无需进行去对称化处理。该技术利用高斯、Wishart和Ginibre系综的谱，以及多体量子系统的谱进行了验证。
英文摘要
The spectral fluctuations in complex quantum systems are modeled in terms of spectra from random matrices. Quantitative agreement with random matrices holds only when the quantum spectrum is a pure sequence, and not a composite spectrum that mixes levels from different symmetry sectors. It was shown earlier that discrete symmetries in composite spectra can be detected using higher-order spacing ratio statistics provided the symmetry sectors are of equal dimensions. The general case is when the symmetry sectors have unequal dimensions, and the symmetries of the Hamiltonian system are unknown or only partially known. In this work, we address how the number of symmetry sectors can be determined from a composite spectrum arising in Hermitian and non-Hermitian settings. A Best Subset Technique is proposed for determining the number of the symmetry sectors by comparing the spectral fluctuations to that of an appropriate random matrix ensemble without requiring de-symmetrization. It is demonstrated using spectra from Gaussian, Wishart and Ginibre ensembles, and also for spectra drawn from many-body quantum systems.
Comments10 pages, 13 figures
