Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from the Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the m...
| Main Authors: | , |
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| Format: | Article |
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IOP
2016
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| Online Access: | https://eprints.nottingham.ac.uk/44637/ |
| _version_ | 1848796962272313344 |
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| author | Truong, K. Ossipov, A. |
| author_facet | Truong, K. Ossipov, A. |
| author_sort | Truong, K. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from the Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the moments and the distribution function of the eigenvectors components for a generic matrix W. We show that specific choices of W can modify significantly the nature of the eigenvectors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations. |
| first_indexed | 2025-11-14T19:56:19Z |
| format | Article |
| id | nottingham-44637 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:56:19Z |
| publishDate | 2016 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-446372020-05-04T17:35:56Z https://eprints.nottingham.ac.uk/44637/ Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices Truong, K. Ossipov, A. We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from the Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the moments and the distribution function of the eigenvectors components for a generic matrix W. We show that specific choices of W can modify significantly the nature of the eigenvectors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations. IOP 2016-02-23 Article PeerReviewed Truong, K. and Ossipov, A. (2016) Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. Journal of Physics A: Mathematical and Theoretical, 49 (14). p. 145005. ISSN 1751-8121 http://iopscience.iop.org/article/10.1088/1751-8113/49/14/145005/meta doi:10.1088/1751-8113/49/14/145005 doi:10.1088/1751-8113/49/14/145005 |
| spellingShingle | Truong, K. Ossipov, A. Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title | Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title_full | Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title_fullStr | Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title_full_unstemmed | Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title_short | Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices |
| title_sort | statistics of eigenvectors in the deformed gaussian unitary ensemble of random matrices |
| url | https://eprints.nottingham.ac.uk/44637/ https://eprints.nottingham.ac.uk/44637/ https://eprints.nottingham.ac.uk/44637/ |