Families of isospectral and isoscattering quantum graphs
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918030437515264 |
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| author | Kurasov, Pavel Farooq, Omer Ławniczak, Michał Bauch, Szymon Pistol, Mats-Erik de Courcy-Ireland, Matthew Sirko, Leszek |
| author_facet | Kurasov, Pavel Farooq, Omer Ławniczak, Michał Bauch, Szymon Pistol, Mats-Erik de Courcy-Ireland, Matthew Sirko, Leszek |
| contents | A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departure from the original approach pioneered by Sunada, where isospectral graphs are obtained as quotients of a certain large symmetric graph. Using the M-function formalism and the symmetries of the graph itself we construct isospectral and isoscattering pairs. In our novel approach isospectral pairs do not need to be embedded into a larger symmetric graph as in Sunada's approach. We demonstrate that the introduced formalism can also be extended to graphs with dissipation. The theoretical predictions are validated experimentally using microwave networks emulating open quantum graphs with dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of isospectral and isoscattering quantum graphs Kurasov, Pavel Farooq, Omer Ławniczak, Michał Bauch, Szymon Pistol, Mats-Erik de Courcy-Ireland, Matthew Sirko, Leszek Quantum Physics A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departure from the original approach pioneered by Sunada, where isospectral graphs are obtained as quotients of a certain large symmetric graph. Using the M-function formalism and the symmetries of the graph itself we construct isospectral and isoscattering pairs. In our novel approach isospectral pairs do not need to be embedded into a larger symmetric graph as in Sunada's approach. We demonstrate that the introduced formalism can also be extended to graphs with dissipation. The theoretical predictions are validated experimentally using microwave networks emulating open quantum graphs with dissipation. |
| title | Families of isospectral and isoscattering quantum graphs |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.16621 |