Spectral statistics of preferred orientation quantum graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912524843089920 |
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| author | Band, Ram Exner, Pavel Goel, Divya Strauss, Aviya |
| author_facet | Band, Ram Exner, Pavel Goel, Divya Strauss, Aviya |
| contents | We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles, one encounters some deviations. We point out these discrepancies and demonstrate that they occur in various graphs and even for Neumann-Kirchhoff vertex conditions, which was overlooked so far. Detailed explanations and computations are provided for this phenomena. To achieve this, we explore the combinatorics of periodic orbits, with a particular emphasis on counting Eulerian cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral statistics of preferred orientation quantum graphs Band, Ram Exner, Pavel Goel, Divya Strauss, Aviya Spectral Theory Mathematical Physics 81Q35, 47B93 We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles, one encounters some deviations. We point out these discrepancies and demonstrate that they occur in various graphs and even for Neumann-Kirchhoff vertex conditions, which was overlooked so far. Detailed explanations and computations are provided for this phenomena. To achieve this, we explore the combinatorics of periodic orbits, with a particular emphasis on counting Eulerian cycles. |
| title | Spectral statistics of preferred orientation quantum graphs |
| topic | Spectral Theory Mathematical Physics 81Q35, 47B93 |
| url | https://arxiv.org/abs/2508.04869 |