Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911506493341696 |
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| author | Christiansen, T. J. Datchev, K. Yang, M. |
| author_facet | Christiansen, T. J. Datchev, K. Yang, M. |
| contents | We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we reduce to prior results in black-box scattering while for non-integral total flux we build on the corresponding techniques using an appropriately chosen model resolvent. The resolvent expansion can be used to obtain long-time wave asymptotics for the Aharonov--Bohm Hamiltonian with multiple poles. An interesting phenomenon is that if the total flux is an integer then the scattering resembles even-dimensional Euclidean scattering, while if it is half an odd integer then it resembles odd-dimensional Euclidean scattering. The behavior for other values of total flux thus provides an `interpolation' between these. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian Christiansen, T. J. Datchev, K. Yang, M. Analysis of PDEs Mathematical Physics Spectral Theory We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we reduce to prior results in black-box scattering while for non-integral total flux we build on the corresponding techniques using an appropriately chosen model resolvent. The resolvent expansion can be used to obtain long-time wave asymptotics for the Aharonov--Bohm Hamiltonian with multiple poles. An interesting phenomenon is that if the total flux is an integer then the scattering resembles even-dimensional Euclidean scattering, while if it is half an odd integer then it resembles odd-dimensional Euclidean scattering. The behavior for other values of total flux thus provides an `interpolation' between these. |
| title | Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2408.03233 |