Simple view
Full metadata view
Authors
Statistics
Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics
Following our recent letter [1], we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general formulas for the spectral density and the eigenvector correlation function for large N and for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations.
cris.lastimport.scopus | 2024-04-07T17:15:47Z | |
dc.abstract.en | Following our recent letter [1], we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general formulas for the spectral density and the eigenvector correlation function for large N and for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations. | 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 | 2015-07-18T09:48:22Z | |
dc.date.available | 2015-07-18T09:48:22Z | |
dc.date.issued | 2015 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.admin | [AB] Tarnowski, Wojciech 50000139 | |
dc.description.admin | [AU] Burda, Zdzisław [SAP11013494] | |
dc.description.physical | 421-447 | pl |
dc.description.publication | 2 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 897 | pl |
dc.identifier.doi | 10.1016/j.nuclphysb.2015.06.002 | pl |
dc.identifier.eissn | 1873-1562 | pl |
dc.identifier.issn | 0550-3213 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/13332 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Dodaję tylko opis bibliograficzny | * |
dc.rights.licence | CC-BY | |
dc.rights.uri | * | |
dc.share.type | otwarte czasopismo | |
dc.subtype | Article | pl |
dc.title | Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics | pl |
dc.title.journal | Nuclear Physics. B | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |