Kohei Kawabata, Zhenyu Xiao, Tomi Ohtsuki, Ryuichi Shindou
{"title":"Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems","authors":"Kohei Kawabata, Zhenyu Xiao, Tomi Ohtsuki, Ryuichi Shindou","doi":"10.1103/prxquantum.4.040312","DOIUrl":null,"url":null,"abstract":"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","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":"9 1","pages":"0"},"PeriodicalIF":11.0000,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"PRX quantum : a Physical Review journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/prxquantum.4.040312","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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