{"title":"单模块圆形集合的特征相分布","authors":"Shinsuke Nishigaki","doi":"10.1093/ptep/ptae018","DOIUrl":null,"url":null,"abstract":"Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe Hanada and Watanabe [1] recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (β = 2), supported by explicit examples at small N and by numerical samplings at larger N. In this letter, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (β = 1) and selfdual (β = 4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Eigenphase distributions of unimodular circular ensembles\",\"authors\":\"Shinsuke Nishigaki\",\"doi\":\"10.1093/ptep/ptae018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe Hanada and Watanabe [1] recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (β = 2), supported by explicit examples at small N and by numerical samplings at larger N. In this letter, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (β = 1) and selfdual (β = 4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1093/ptep/ptae018\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1093/ptep/ptae018","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Eigenphase distributions of unimodular circular ensembles
Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe Hanada and Watanabe [1] recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (β = 2), supported by explicit examples at small N and by numerical samplings at larger N. In this letter, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (β = 1) and selfdual (β = 4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.
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