A modified local Weyl law and spectral comparison results for $δ'$-coupling conditions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908292232511488 |
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| author | Bifulco, Patrizio Kerner, Joachim |
| author_facet | Bifulco, Patrizio Kerner, Joachim |
| contents | We study Schrödinger operators on compact finite metric graphs subject to $δ'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing $δ'$-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in [arXiv:2212.12531].
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| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A modified local Weyl law and spectral comparison results for $δ'$-coupling conditions Bifulco, Patrizio Kerner, Joachim Spectral Theory Mathematical Physics 34L05, 81Q35, 34L15, 34L20 We study Schrödinger operators on compact finite metric graphs subject to $δ'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing $δ'$-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in [arXiv:2212.12531]. . |
| title | A modified local Weyl law and spectral comparison results for $δ'$-coupling conditions |
| topic | Spectral Theory Mathematical Physics 34L05, 81Q35, 34L15, 34L20 |
| url | https://arxiv.org/abs/2407.21719 |