NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES
We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: <em>f(x)</em>) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions...
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| Format: | Article |
| Language: | English |
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CTU Central Library
2017-12-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/4481 |
| _version_ | 1818152280066621440 |
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| author | Sachin Kumar Zafar Ahmed |
| author_facet | Sachin Kumar Zafar Ahmed |
| author_sort | Sachin Kumar |
| collection | DOAJ |
| description | We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: <em>f(x)</em>) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions <em>p(s)</em> of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as <em>αs</em> where <em>α</em> depends on the choice of the PDF. More interestingly when <em>f</em>(<em>x</em>) = <em>xe</em><sup>−x<sup>2</sup></sup> (<em>f</em>(0) = 0), we get cubic level repulsion near s = 0: <em>p(s)</em> ~ s<sup>3</sup>e<sup>−s<sup>2</sup></sup>.We also derive the distribution of eigenvalues <em>D</em>(ε) for these matrices. |
| first_indexed | 2024-12-11T13:52:12Z |
| format | Article |
| id | doaj.art-0b25e4159d1746ffafcdd67e4fc1e8de |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-12-11T13:52:12Z |
| publishDate | 2017-12-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-0b25e4159d1746ffafcdd67e4fc1e8de2022-12-22T01:04:12ZengCTU Central LibraryActa Polytechnica1210-27091805-23632017-12-0157641842310.14311/AP.2017.57.04184037NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICESSachin Kumar0Zafar Ahmed1Bhabha Atomic Research Centre, MumbaiNuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, IndiaWe investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: <em>f(x)</em>) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions <em>p(s)</em> of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as <em>αs</em> where <em>α</em> depends on the choice of the PDF. More interestingly when <em>f</em>(<em>x</em>) = <em>xe</em><sup>−x<sup>2</sup></sup> (<em>f</em>(0) = 0), we get cubic level repulsion near s = 0: <em>p(s)</em> ~ s<sup>3</sup>e<sup>−s<sup>2</sup></sup>.We also derive the distribution of eigenvalues <em>D</em>(ε) for these matrices.https://ojs.cvut.cz/ojs/index.php/ap/article/view/4481real symmetric matricesWigner surmise |
| spellingShingle | Sachin Kumar Zafar Ahmed NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES Acta Polytechnica real symmetric matrices Wigner surmise |
| title | NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES |
| title_full | NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES |
| title_fullStr | NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES |
| title_full_unstemmed | NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES |
| title_short | NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES |
| title_sort | new spectral statistics for ensembles of 2 2 real symmetric random matrices |
| topic | real symmetric matrices Wigner surmise |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/4481 |
| work_keys_str_mv | AT sachinkumar newspectralstatisticsforensemblesof22realsymmetricrandommatrices AT zafarahmed newspectralstatisticsforensemblesof22realsymmetricrandommatrices |