Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909515225497600 |
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| author | Gallone, Matteo Michelangeli, Alessandro Noja, Diego |
| author_facet | Gallone, Matteo Michelangeli, Alessandro Noja, Diego |
| contents | We characterise the families of self-adjoint Dirac and Schrödinger operators with Aharonov-Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short-scale boundary condition of self-adjointness. This ensures that the scattering length of the Aharonov-Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac-AB operators is mapped, in the non-relativistic limit, into the physically relevant sub-family of $s$-wave, angular-momentum-commuting, Schrö\-dinger-AB Hamiltonians with relativistic Dirac approximants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields Gallone, Matteo Michelangeli, Alessandro Noja, Diego Mathematical Physics Spectral Theory Quantum Physics 81Q10, 34L40, 47B25, 47N50 We characterise the families of self-adjoint Dirac and Schrödinger operators with Aharonov-Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short-scale boundary condition of self-adjointness. This ensures that the scattering length of the Aharonov-Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac-AB operators is mapped, in the non-relativistic limit, into the physically relevant sub-family of $s$-wave, angular-momentum-commuting, Schrö\-dinger-AB Hamiltonians with relativistic Dirac approximants. |
| title | Non-relativistic limit of Dirac Hamiltonians with Aharonov-Bohm fields |
| topic | Mathematical Physics Spectral Theory Quantum Physics 81Q10, 34L40, 47B25, 47N50 |
| url | https://arxiv.org/abs/2502.20318 |