| Autor: |
Xiao, Zhenyu, Shindou, Ryuichi, Kawabata, Kohei |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Phys. Rev. Research 6, 023303 (2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevResearch.6.023303 |
| Popis: |
Random matrix theory is a powerful tool for understanding spectral correlations inherent in quantum chaotic systems. Despite diverse applications of non-Hermitian random matrix theory, the role of symmetry remains to be fully established. Here, we comprehensively investigate the impact of symmetry on the level statistics around the spectral origin -- hard-edge statistics -- and expand the classification of spectral statistics to encompass all the 38 symmetry classes of non-Hermitian random matrices. Within this classification, we discern 28 symmetry classes characterized by distinct hard-edge statistics from the level statistics in the bulk of spectra, which are further categorized into two groups, namely the Altland-Zirnbauer$_0$ classification and beyond. We introduce and elucidate quantitative measures capturing the universal hard-edge statistics for all the symmetry classes. Furthermore, through extensive numerical calculations, we study various open quantum systems in different symmetry classes, including quadratic and many-body Lindbladians, as well as non-Hermitian Hamiltonians. We show that these systems manifest the same hard-edge statistics as random matrices and that their ensemble-average spectral distributions around the origin exhibit emergent symmetry conforming to the random-matrix behavior. Our results establish a comprehensive understanding of non-Hermitian random matrix theory and are useful in detecting quantum chaos or its absence in open quantum systems. |
| Databáze: |
arXiv |
| Externí odkaz: |
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