Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
We consider eigenvectors of the Hamiltonian H0 perturbed by a generic perturbation V modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the super-symmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in V and valid...
| Main Authors: | , |
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| Format: | Article |
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European Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/39396/ |
| _version_ | 1848795827389071360 |
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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 consider eigenvectors of the Hamiltonian H0 perturbed by a generic perturbation V modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the super-symmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in V and valid for an arbitrary deterministic H0. Further we generalise them to the case of a random H0, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations. |
| first_indexed | 2025-11-14T19:38:16Z |
| format | Article |
| id | nottingham-39396 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:38:16Z |
| publishDate | 2016 |
| publisher | European Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-393962020-05-04T18:26:48Z https://eprints.nottingham.ac.uk/39396/ Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach Truong, K. Ossipov, A. We consider eigenvectors of the Hamiltonian H0 perturbed by a generic perturbation V modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the super-symmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in V and valid for an arbitrary deterministic H0. Further we generalise them to the case of a random H0, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations. European Physical Society 2016-12-09 Article PeerReviewed Truong, K. and Ossipov, A. (2016) Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach. EPL, 116 (3). 37002/1-37002/6. ISSN 1286-4854 http://dx.doi.org/10.1209/0295-5075/116/37002 doi:10.1209/0295-5075/116/37002 doi:10.1209/0295-5075/116/37002 |
| spellingShingle | Truong, K. Ossipov, A. Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title | Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title_full | Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title_fullStr | Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title_full_unstemmed | Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title_short | Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| title_sort | eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach |
| url | https://eprints.nottingham.ac.uk/39396/ https://eprints.nottingham.ac.uk/39396/ https://eprints.nottingham.ac.uk/39396/ |