Semiclassical shape resonances for magnetic Stark Hamiltonians
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915896979619840 |
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| author | Kameoka, Kentaro Yoshida, Naoya |
| author_facet | Kameoka, Kentaro Yoshida, Naoya |
| contents | We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that the scalar potential has potential wells, the existence of a one-to-one correspondence between shape resonances of the Hamiltonian and discrete eigenvalues of a certain reference operator is proved. This implies the Weyl law for the number of resonances and the asymptotic behavior of the real parts of resonances near the bottom of a potential well. Resonances are studied as complex eigenvalues of complex distorted Hamiltonians, which is defined by the complex translation outside a compact set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27196 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiclassical shape resonances for magnetic Stark Hamiltonians Kameoka, Kentaro Yoshida, Naoya Mathematical Physics Analysis of PDEs Spectral Theory 81Q20, 81U24, 81U26 We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that the scalar potential has potential wells, the existence of a one-to-one correspondence between shape resonances of the Hamiltonian and discrete eigenvalues of a certain reference operator is proved. This implies the Weyl law for the number of resonances and the asymptotic behavior of the real parts of resonances near the bottom of a potential well. Resonances are studied as complex eigenvalues of complex distorted Hamiltonians, which is defined by the complex translation outside a compact set. |
| title | Semiclassical shape resonances for magnetic Stark Hamiltonians |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory 81Q20, 81U24, 81U26 |
| url | https://arxiv.org/abs/2603.27196 |