Average Spectral Density of Multiparametric Gaussian Ensembles of Complex Matrices
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arXiv
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| Format: | Preprint |
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2023
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| author | Ansari, Mohd. Gayas Shukla, Pragya |
| author_facet | Ansari, Mohd. Gayas Shukla, Pragya |
| contents | A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the system, the ensemble parameters must be determined from the system parameters. This in turn makes its necessary to analyze a wide range of multi-parametric ensembles with different kinds of matrix elements distributions. The spectral statistics of such ensembles is not only system-dependent but also non-ergodic as well as non-stationary.
A change in system conditions can cause a change in the ensemble parameters resulting an evolution of the ensemble density and it is not sufficient to know the statistics for a given set of system conditions. This motivates us to theoretically analyze a multiparametric evolution of the ensemble averaged spectral density of a multiparametric Gaussian ensemble on the complex plane. Our analysis reveals the existence of an evolutionary route common to the ensembles belonging to same global constraint class and thereby derives a complexity parameter dependent formulation of the spectral density for the non-equilibrium regime of the spectral statistics, away from Ginibre equilibrium limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Average Spectral Density of Multiparametric Gaussian Ensembles of Complex Matrices Ansari, Mohd. Gayas Shukla, Pragya Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the system, the ensemble parameters must be determined from the system parameters. This in turn makes its necessary to analyze a wide range of multi-parametric ensembles with different kinds of matrix elements distributions. The spectral statistics of such ensembles is not only system-dependent but also non-ergodic as well as non-stationary. A change in system conditions can cause a change in the ensemble parameters resulting an evolution of the ensemble density and it is not sufficient to know the statistics for a given set of system conditions. This motivates us to theoretically analyze a multiparametric evolution of the ensemble averaged spectral density of a multiparametric Gaussian ensemble on the complex plane. Our analysis reveals the existence of an evolutionary route common to the ensembles belonging to same global constraint class and thereby derives a complexity parameter dependent formulation of the spectral density for the non-equilibrium regime of the spectral statistics, away from Ginibre equilibrium limit. |
| title | Average Spectral Density of Multiparametric Gaussian Ensembles of Complex Matrices |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2301.08850 |