Eigenphase distributions of unimodular circular ensembles

Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe 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 le...

Full description

Saved in:
Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2024; no. 2
Main Author Nishigaki, Shinsuke
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.02.2024
Subjects
Eigenvalues
Online AccessGet full text
ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptae018

Cover

Abstract Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe 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.
AbstractList Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe 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.
Author Nishigaki, Shinsuke
Author_xml – sequence: 1
  givenname: Shinsuke
  surname: Nishigaki
  fullname: Nishigaki, Shinsuke
  email: mochizuki@riko.shimane-u.ac.jp
BookMark eNp9kLFOwzAQhi1UJErpxgNEYmAhcK6d2B5R1QJSJRaYLTu5gKvUDnYy8PakpAMTy90v3ae703dJZj54JOSawj0FxR66HruxGAQqz8h8BQXkTFE6-5MvyDKlPQBQEAI4nRO1cR_ou0-TMKtd6qOzQ--CT1lossG7Q6iH1sSscrH6DegTHmyL6YqcN6ZNuDz1BXnfbt7Wz_nu9ell_bjLKy5Yn1MKvEajLK8tSiUVgGiUklAyI6wAYQwzTFoxTkSJFcrxMZTVqhS24KxgC3Iz7e1i-Bow9XofhujHk5pRQbkqeSlG6m6iqhhSitjoLrqDid-agj760Uc_-uRnxG8nPAzd_-QPcYBooA
Cites_doi 10.1103/PhysRevLett.124.212502
10.1063/1.1703773
10.1146/annurev.ns.16.120166.001101
10.1515/9781400835416
10.1016/j.laa.2021.02.031
10.1103/PhysRevE.59.1489
10.1007/s00220-008-0484-7
10.1063/1.1703863
ContentType Journal Article
Copyright The Author(s) 2024. Published by Oxford University Press on behalf of the Physical Society of Japan. 2024
The Author(s) 2024. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: The Author(s) 2024. Published by Oxford University Press on behalf of the Physical Society of Japan. 2024
– notice: The Author(s) 2024. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID TOX
AAYXX
CITATION
3V.
7XB
88I
8FK
ABUWG
AFKRA
AZQEC
BENPR
CCPQU
DWQXO
GNUQQ
HCIFZ
M2P
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
Q9U
DOI 10.1093/ptep/ptae018
DatabaseName Oxford Journals Open Access Collection
CrossRef
ProQuest Central (Corporate)
ProQuest Central (purchase pre-March 2016)
Science Database (Alumni Edition)
ProQuest Central (Alumni) (purchase pre-March 2016)
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest One Community College
ProQuest Central
ProQuest Central Student
SciTech Premium Collection
Science Database
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
ProQuest Central Basic
DatabaseTitle CrossRef
Publicly Available Content Database
ProQuest Science Journals (Alumni Edition)
ProQuest Central Student
ProQuest One Academic Middle East (New)
ProQuest Central Basic
ProQuest Central Essentials
ProQuest Science Journals
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: TOX
  name: Oxford Journals Open Access Collection
  url: https://academic.oup.com/journals/
  sourceTypes: Publisher
– sequence: 2
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 2050-3911
ExternalDocumentID 10_1093_ptep_ptae018
10.1093/ptep/ptae018
GroupedDBID .I3
0R~
4.4
5VS
AAFWJ
AAMVS
AAPPN
AAPXW
AAVAP
ABEJV
ABGNP
ABPTD
ABXVV
ACGFS
ADHZD
AENEX
AENZO
AFPKN
AFULF
AIBLX
ALMA_UNASSIGNED_HOLDINGS
ALUQC
AMNDL
BAYMD
BTTYL
CIDKT
D~K
EBS
EJD
ER.
GROUPED_DOAJ
H13
IAO
ISR
ITC
KQ8
KSI
M~E
O9-
OAWHX
OJQWA
OK1
PEELM
RHF
ROL
ROX
RXO
TOX
~D7
88I
AAYXX
ABUWG
AFKRA
AZQEC
BENPR
CCPQU
CITATION
DWQXO
GNUQQ
HCIFZ
M2P
PHGZM
PHGZT
PIMPY
3V.
7XB
8FK
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c473t-1104dea9b4dbe8989007f998063a7b707aa3a38b789076ece8704e8c267b54353
IEDL.DBID BENPR
ISSN 2050-3911
IngestDate Mon Jun 30 12:25:21 EDT 2025
Tue Jul 01 02:09:16 EDT 2025
Fri Jan 31 08:06:30 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
License This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
https://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c473t-1104dea9b4dbe8989007f998063a7b707aa3a38b789076ece8704e8c267b54353
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
OpenAccessLink https://www.proquest.com/docview/3171496467?pq-origsite=%requestingapplication%
PQID 3171496467
PQPubID 7121340
ParticipantIDs proquest_journals_3171496467
crossref_primary_10_1093_ptep_ptae018
oup_primary_10_1093_ptep_ptae018
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2024-02-01
PublicationDateYYYYMMDD 2024-02-01
PublicationDate_xml – month: 02
  year: 2024
  text: 2024-02-01
  day: 01
PublicationDecade 2020
PublicationPlace Oxford
PublicationPlace_xml – name: Oxford
PublicationTitle Progress of theoretical and experimental physics
PublicationYear 2024
Publisher Oxford University Press
Publisher_xml – name: Oxford University Press
References Fasi (2024032818430116000_bib2) 2021
Forrester (2024032818430116000_bib10) 2010
Götze (2024032818430116000_bib5) 2008; 281
Dyson (2024032818430116000_bib6) 1962; 3
Selberg (2024032818430116000_bib8) 1944; 26
Akemann (2024032818430116000_bib4) 1999; 59
Hanada (2024032818430116000_bib1)
Morris (2024032818430116000_bib9) 1982
Rosenzweig (2024032818430116000_bib3) 1963
Dyson (2024032818430116000_bib7) 1962; 3
References_xml – volume-title: Constant term identities for finite and affine root systems: conjectures and theorems
  year: 1982
  ident: 2024032818430116000_bib9
  doi: 10.1103/PhysRevLett.124.212502
– volume: 3
  start-page: 140
  year: 1962
  ident: 2024032818430116000_bib7
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1703773
– volume: 26
  start-page: 71
  year: 1944
  ident: 2024032818430116000_bib8
  publication-title: Norsk Mat. Tidsskr.
– ident: 2024032818430116000_bib1
  doi: 10.1146/annurev.ns.16.120166.001101
– volume-title: Log-Gases and Random Matrices
  year: 2010
  ident: 2024032818430116000_bib10
  doi: 10.1515/9781400835416
– start-page: 297
  volume-title: Linear Algebra Appl.
  year: 2021
  ident: 2024032818430116000_bib2
  doi: 10.1016/j.laa.2021.02.031
– volume-title: Statistical Physics (Brandeis Summer Institute, 1962)
  year: 1963
  ident: 2024032818430116000_bib3
  article-title: Statistical mechanics of equally likely quantum systems
– volume: 59
  start-page: 1489
  year: 1999
  ident: 2024032818430116000_bib4
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.59.1489
– volume: 281
  start-page: 203
  year: 2008
  ident: 2024032818430116000_bib5
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s00220-008-0484-7
– volume: 3
  start-page: 1199
  year: 1962
  ident: 2024032818430116000_bib6
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1703863
SSID ssj0001077041
Score 2.292225
Snippet Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of...
SourceID proquest
crossref
oup
SourceType Aggregation Database
Index Database
Publisher
SubjectTerms Eigenvalues
Title Eigenphase distributions of unimodular circular ensembles
URI https://www.proquest.com/docview/3171496467
Volume 2024
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV09T8MwELWgXVj4RhRK5QFGq4ntxPGEALWqGApCrdQtsmNXIEGaNun_55w4KiyweEm83OnuvbPP9xC6TUyo3Zg6EscRhQIlsUQGzBAjYiPdtBWt626LaTyZ8-dFtPAHbqVvq2xzYp2ozSpzZ-RD5pS6ZQxxfV-siVONcrerXkJjH3UhBSdQfHUfR9PXt90pSyBEwEPf8Q7V-7CobAGLsoHT-fiBRb_et7UJuUaZ8TE69PQQPzT-PEF7Nj9FR54qYh-I5RmSIzdFs3gHDMLGzb71slUlXi3xNgcHGNdfirOPTd1oiqFatV_605bnaD4ezZ4mxKsgkIwLVhHAZ26skpobbZ3YI6D6Eook4BZKaBEIpZhiiXYvWkVsMwsRyG2S0VjoCMgQu0CdfJXbS4Sp1EZImlGH6sCLEsUjHbIQNnGhKe-hu9YeadEMu0ibS2qWOrul3m49hMFY__zSby2Z-qgo050Pr_7-fI0OKJCHpju6jzrVZmtvAPwrPfAeHtTFM6yzl8U3pduyEQ
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwED5V7QALb0ShgAcYI1LbjZMBIR6tWloqhFqJLcSxK5CgDU0rxJ_iN3JOHBUWmLpkib3c67uzz_cBnPiqLs2YOsfzGhQLFF87gcuUo4SnAjNtRcqs26LvtYf89rHxWIKv4i2MaassYmIWqNUkNmfkZ8wwdQce-vVF8u4Y1ihzu1pQaORm0dWfH1iypeedG9TvKaWt5uC67VhWASfmgs0cxDuudBRIrqQ25ImIkiMsOhCrIyGFK6KIRcyX5oWo8HSs0aK59mPqCdngGUsEhvwKZ1jKlKFy1ezfPyxOdVyBq-u2w94N2Fky0wl-Iu0aXpEf2PfrPV0BABmqtTZgzaaj5DK3n00o6fEWrNvUlFjHT7chaJqpnckzYh5RZtaupclKyWRE5mNUuDL9rCR-mWaNrQSrY_0mX3W6A8OlyGcXyuPJWO8BoYFUIqAxNVkE5mF-xBuyzuq4iQtJeRVOC3mEST5cI8wvxVlo5BZauVWBoLD-WVIrJBlaL0zDhc3s__37GFbag7te2Ov0uwewSjFxyTuza1CeTef6EBOPmTyy2ibwtGwD-wbBy-tZ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Eigenphase+distributions+of+unimodular+circular+ensembles&rft.jtitle=Progress+of+theoretical+and+experimental+physics&rft.au=Nishigaki%2C+Shinsuke&rft.date=2024-02-01&rft.pub=Oxford+University+Press&rft.eissn=2050-3911&rft.volume=2024&rft.issue=2&rft_id=info:doi/10.1093%2Fptep%2Fptae018&rft.externalDocID=10.1093%2Fptep%2Fptae018
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2050-3911&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2050-3911&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2050-3911&client=summon