Cwikel-Lieb-Rozenblum type estimates for the Pauli and magnetic Schrödinger operator in dimension two
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913814650290176 |
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| author | Baur, Matthias Kovarik, Hynek |
| author_facet | Baur, Matthias Kovarik, Hynek |
| contents | We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of Pauli operators in dimension two. The resulting upper bound is sharp both in the weak as well as in the strong coupling limit. We also derive different upper bounds for magnetic Schrödinger operators. The nature of the two estimates depends on whether or not the spin-orbit coupling is taken into account. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cwikel-Lieb-Rozenblum type estimates for the Pauli and magnetic Schrödinger operator in dimension two Baur, Matthias Kovarik, Hynek Mathematical Physics Spectral Theory We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of Pauli operators in dimension two. The resulting upper bound is sharp both in the weak as well as in the strong coupling limit. We also derive different upper bounds for magnetic Schrödinger operators. The nature of the two estimates depends on whether or not the spin-orbit coupling is taken into account. |
| title | Cwikel-Lieb-Rozenblum type estimates for the Pauli and magnetic Schrödinger operator in dimension two |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2505.00428 |