Ornstein-Uhlenbeck diffusion of hermitian and non-hermitian matrices - unexpected links
| Autor: | Jacek Grela, Piotr Warchoł, Wojciech Tarnowski, Maciej A. Nowak, Jean-Paul Blaizot |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Gaussian FOS: Physical sciences 01 natural sciences Unitary state 010305 fluids & plasmas symbols.namesake 0103 physical sciences FOS: Mathematics Statistical physics 010306 general physics Eigenvalues and eigenvectors Mathematical Physics Mathematics Variable (mathematics) Probability (math.PR) Statistical and Nonlinear Physics Ornstein–Uhlenbeck process Mathematical Physics (math-ph) Coupling (probability) Nonlinear Sciences - Chaotic Dynamics Hermitian matrix Flow (mathematics) symbols Statistics Probability and Uncertainty Chaotic Dynamics (nlin.CD) Mathematics - Probability |
| Popis: | 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. 21 pages, 4 figures, submitted to J. Stat. Phys |
| Databáze: | OpenAIRE |
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