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Ornstein–Uhlenbeck diffusion of hermitian and non-hermitian matrices : unexpected links
We compare the Ornstein–Uhlenbeck process for the Gaussian unitary ensemble to its non-hermitian counterpart—for the complex Ginibre ensemble. We exploit the mathematical framework based on the generalized Green’s functions, which involves a new, hidden complex variable, in comparison to the standard treatment of the resolvents. This new variable turns out to be crucial to understand the pattern of the evolution of non-hermitian systems. The new feature is the emergence of the coupling between the flow of eigenvalues and that of left/right eigenvectors. We analyze local and global equilibria for both systems. Finally, we highlight some unexpected links between both ensembles.
cris.lastimport.wos | 2024-04-10T00:36:25Z | |
dc.abstract.en | We compare the Ornstein–Uhlenbeck process for the Gaussian unitary ensemble to its non-hermitian counterpart—for the complex Ginibre ensemble. We exploit the mathematical framework based on the generalized Green’s functions, which involves a new, hidden complex variable, in comparison to the standard treatment of the resolvents. This new variable turns out to be crucial to understand the pattern of the evolution of non-hermitian systems. The new feature is the emergence of the coupling between the flow of eigenvalues and that of left/right eigenvectors. We analyze local and global equilibria for both systems. Finally, we highlight some unexpected links between both ensembles. | pl |
dc.affiliation | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego | pl |
dc.contributor.author | Blaizot, Jean-Paul | pl |
dc.contributor.author | Grela, Jacek - 195052 | pl |
dc.contributor.author | Nowak, Maciej - 131031 | pl |
dc.contributor.author | Tarnowski, Wojciech - 205320 | pl |
dc.contributor.author | Warchoł, Piotr - 106215 | pl |
dc.date.accessioned | 2017-01-03T11:23:42Z | |
dc.date.available | 2017-01-03T11:23:42Z | |
dc.date.issued | 2016 | pl |
dc.description.number | 5 | pl |
dc.description.volume | 2016 | pl |
dc.identifier.articleid | 054037 | pl |
dc.identifier.doi | 10.1088/1742-5468/2016/05/054037 | pl |
dc.identifier.eissn | 1742-5468 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/34781 | |
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 | Ornstein–Uhlenbeck diffusion of hermitian and non-hermitian matrices : unexpected links | pl |
dc.title.journal | Journal of Statistical Mechanics | pl |
dc.title.volume | Special Issue on Unsolved Problems of Noise in Physics, Biology and Technology | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |