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Relationship between scattering matrix and spectrum of quantum graphs
We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph and the associated unitary scattering operator. We prove that the statistics of level spacings and moments of observations in the eigenbases coincide in the limit that all bond lengths approach...
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| Main Authors: | , |
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| Format: | Default Article |
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2010
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| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/15453 |
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| _version_ | 1818173414926450688 |
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| author | G. Berkolaiko Brian Winn |
| author_facet | G. Berkolaiko Brian Winn |
| author_sort | G. Berkolaiko (7159685) |
| collection | Figshare |
| description | We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph and the associated unitary scattering operator. We prove that the statistics of level spacings and moments of observations in the eigenbases coincide in the limit that all bond lengths approach a positive constant value. © 2010 American Mathematical Society. |
| format | Default Article |
| id | rr-article-9385307 |
| institution | Loughborough University |
| publishDate | 2010 |
| record_format | Figshare |
| spelling | rr-article-93853072010-01-01T00:00:00Z Relationship between scattering matrix and spectrum of quantum graphs G. Berkolaiko (7159685) Brian Winn (1247334) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph and the associated unitary scattering operator. We prove that the statistics of level spacings and moments of observations in the eigenbases coincide in the limit that all bond lengths approach a positive constant value. © 2010 American Mathematical Society. 2010-01-01T00:00:00Z Text Journal contribution 2134/15453 https://figshare.com/articles/journal_contribution/Relationship_between_scattering_matrix_and_spectrum_of_quantum_graphs/9385307 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified G. Berkolaiko Brian Winn Relationship between scattering matrix and spectrum of quantum graphs |
| title | Relationship between scattering matrix and spectrum of quantum graphs |
| title_full | Relationship between scattering matrix and spectrum of quantum graphs |
| title_fullStr | Relationship between scattering matrix and spectrum of quantum graphs |
| title_full_unstemmed | Relationship between scattering matrix and spectrum of quantum graphs |
| title_short | Relationship between scattering matrix and spectrum of quantum graphs |
| title_sort | relationship between scattering matrix and spectrum of quantum graphs |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/15453 |