Dysonian dynamics of the Ginibre ensemble

2014
journal article
article
32
cris.lastimport.wos2024-04-09T22:06:37Z
dc.abstract.enWe study the time evolution of Ginibre matrices whose elements undergo Brownian motion. The non-Hermitian character of the Ginibre ensemble binds the dynamics of eigenvalues to the evolution of eigenvectors in a nontrivial way, leading to a system of coupled nonlinear equations resembling those for turbulent systems. We formulate a mathematical framework allowing simultaneous description of the flow of eigenvalues and eigenvectors, and we unravel a hidden dynamics as a function of a new complex variable, which in the standard description is treated as a regulator only. We solve the evolution equations for large matrices and demonstrate that the nonanalytic behavior of the Green’s functions is associated with a shock wave stemming from a Burgers-like equation describing correlations of eigenvectors. We conjecture that the hidden dynamics that we observe for the Ginibre ensemble is a general feature of non-Hermitian random matrix models and is relevant to related physical applications.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorBurda, Zdzisław - 127492 pl
dc.contributor.authorGrela, Jacek - 195052 pl
dc.contributor.authorNowak, Maciej - 131031 pl
dc.contributor.authorTarnowski, Wojciechpl
dc.contributor.authorWarchoł, Piotr - 106215 pl
dc.date.accessioned2015-04-28T10:28:56Z
dc.date.available2015-04-28T10:28:56Z
dc.date.issued2014pl
dc.description.admin[AB] Tarnowski, Wojciech 50000139
dc.description.number10pl
dc.description.volume113pl
dc.identifier.articleid104102pl
dc.identifier.doi10.1103/PhysRevLett.113.104102pl
dc.identifier.eissn1079-7114pl
dc.identifier.eissn1092-0145pl
dc.identifier.issn0031-9007pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/5954
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subtypeArticlepl
dc.titleDysonian dynamics of the Ginibre ensemblepl
dc.title.journalPhysical Review Letterspl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-09T22:06:37Z
dc.abstract.enpl
We study the time evolution of Ginibre matrices whose elements undergo Brownian motion. The non-Hermitian character of the Ginibre ensemble binds the dynamics of eigenvalues to the evolution of eigenvectors in a nontrivial way, leading to a system of coupled nonlinear equations resembling those for turbulent systems. We formulate a mathematical framework allowing simultaneous description of the flow of eigenvalues and eigenvectors, and we unravel a hidden dynamics as a function of a new complex variable, which in the standard description is treated as a regulator only. We solve the evolution equations for large matrices and demonstrate that the nonanalytic behavior of the Green’s functions is associated with a shock wave stemming from a Burgers-like equation describing correlations of eigenvectors. We conjecture that the hidden dynamics that we observe for the Ginibre ensemble is a general feature of non-Hermitian random matrix models and is relevant to related physical applications.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Burda, Zdzisław - 127492
dc.contributor.authorpl
Grela, Jacek - 195052
dc.contributor.authorpl
Nowak, Maciej - 131031
dc.contributor.authorpl
Tarnowski, Wojciech
dc.contributor.authorpl
Warchoł, Piotr - 106215
dc.date.accessioned
2015-04-28T10:28:56Z
dc.date.available
2015-04-28T10:28:56Z
dc.date.issuedpl
2014
dc.description.admin
[AB] Tarnowski, Wojciech 50000139
dc.description.numberpl
10
dc.description.volumepl
113
dc.identifier.articleidpl
104102
dc.identifier.doipl
10.1103/PhysRevLett.113.104102
dc.identifier.eissnpl
1079-7114
dc.identifier.eissnpl
1092-0145
dc.identifier.issnpl
0031-9007
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/5954
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subtypepl
Article
dc.titlepl
Dysonian dynamics of the Ginibre ensemble
dc.title.journalpl
Physical Review Letters
dc.typepl
JournalArticle
dspace.entity.type
Publication

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