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Dysonian dynamics of the Ginibre ensemble
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.
cris.lastimport.wos | 2024-04-09T22:06:37Z | |
dc.abstract.en | 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. | pl |
dc.affiliation | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego | pl |
dc.contributor.author | Burda, Zdzisław - 127492 | pl |
dc.contributor.author | Grela, Jacek - 195052 | pl |
dc.contributor.author | Nowak, Maciej - 131031 | pl |
dc.contributor.author | Tarnowski, Wojciech | pl |
dc.contributor.author | Warchoł, Piotr - 106215 | pl |
dc.date.accessioned | 2015-04-28T10:28:56Z | |
dc.date.available | 2015-04-28T10:28:56Z | |
dc.date.issued | 2014 | pl |
dc.description.admin | [AB] Tarnowski, Wojciech 50000139 | |
dc.description.number | 10 | pl |
dc.description.volume | 113 | pl |
dc.identifier.articleid | 104102 | pl |
dc.identifier.doi | 10.1103/PhysRevLett.113.104102 | pl |
dc.identifier.eissn | 1079-7114 | pl |
dc.identifier.eissn | 1092-0145 | pl |
dc.identifier.issn | 0031-9007 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/5954 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Dodaję tylko opis bibliograficzny | * |
dc.rights.licence | bez licencji | |
dc.rights.uri | * | |
dc.subtype | Article | pl |
dc.title | Dysonian dynamics of the Ginibre ensemble | pl |
dc.title.journal | Physical Review Letters | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |