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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.17920 |
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| _version_ | 1866912714422484992 |
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| author | Angelone, Giuliano Asorey, Manuel Ezquerro, Fernando Facchi, Paolo |
| author_facet | Angelone, Giuliano Asorey, Manuel Ezquerro, Fernando Facchi, Paolo |
| contents | We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy operator self-adjoint, and form a four-parameters family that includes the $δ$-potential and the $δ'$-potential as particular cases. We study the parameter dependence of the spectral properties of this system, finding a rich isospectrality structure. We systematically classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isospectrality and non-locality of generalized Dirac combs Angelone, Giuliano Asorey, Manuel Ezquerro, Fernando Facchi, Paolo Quantum Physics We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy operator self-adjoint, and form a four-parameters family that includes the $δ$-potential and the $δ'$-potential as particular cases. We study the parameter dependence of the spectral properties of this system, finding a rich isospectrality structure. We systematically classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation. |
| title | Isospectrality and non-locality of generalized Dirac combs |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.17920 |