非厄米随机矩阵和开放量子系统的奇异值统计

IF 11 Q1 PHYSICS, APPLIED
Kohei Kawabata, Zhenyu Xiao, Tomi Ohtsuki, Ryuichi Shindou
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引用次数: 0

摘要

非厄米随机矩阵的谱统计量作为一种诊断开放量子系统混沌行为的重要工具。本文研究了非厄米随机矩阵中奇异值的统计性质,作为量化耗散量子混沌的有效测度。通过赫米化,揭示了奇异值统计量区别于复特征值统计量的独特特征,并建立了所有38重对称非赫米随机矩阵的奇异值统计量的综合分类。我们还解析地导出了小随机矩阵的奇异值统计量,它很好地描述了大随机矩阵的奇异值统计量,其性质与维格纳猜想类似。此外,我们证明了开放量子多体系统的奇异值遵循随机矩阵统计量,从而识别了开放量子系统中的混沌和不可积性。我们的工作阐明了奇异值统计作为对称的明确指标,并为开放量子系统的统计物理奠定了基础。根据知识共享署名4.0国际许可协议,美国物理学会doi:https://doi.org/10.1103/PRXQuantum.4.040312Published。这项工作的进一步分发必须保持作者的归属和已发表文章的标题,期刊引用和DOI。发表于美国物理学会物理学科标题(PhySH)研究领域开放量子系统量子混沌量子相关,基础与形式化量子统计力学物理系统非厄米系统技术林德布莱德方程随机矩阵理论凝聚态对称性凝聚态物质,材料与应用物理统计物理与热力学量子信息,科学与技术原子,分子与光学
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems

Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random matrices as an effective measure of quantifying dissipative quantum chaos. By means of Hermitization, we reveal the unique characteristics of the singular-value statistics that distinguish them from the complex-eigenvalue statistics, and establish the comprehensive classification of the singular-value statistics for all the 38-fold symmetry classes of non-Hermitian random matrices. We also analytically derive the singular-value statistics of small random matrices, which well describe those of large random matrices in the similar spirit to the Wigner surmise. Furthermore, we demonstrate that singular values of open quantum many-body systems follow the random-matrix statistics, thereby identifying chaos and nonintegrability in open quantum systems. Our work elucidates that the singular-value statistics serve as a clear indicator of symmetry and lay a foundation for statistical physics of open quantum systems.Received 16 July 2023Accepted 20 September 2023DOI:https://doi.org/10.1103/PRXQuantum.4.040312Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasOpen quantum systemsQuantum chaosQuantum correlations, foundations & formalismQuantum statistical mechanicsPhysical SystemsNon-Hermitian systemsTechniquesLindblad equationRandom matrix theorySymmetries in condensed matterCondensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyAtomic, Molecular & Optical
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CiteScore
14.60
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0.00%
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