COUNTING NEGATIVE EIGENVALUES FOR THE MAGNETIC PAULI OPERATOR
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| Název: | COUNTING NEGATIVE EIGENVALUES FOR THE MAGNETIC PAULI OPERATOR |
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| Autoři: | Fournais, SØren, Frank, Rupert L., Goffeng, Magnus, Kachmar, Ayman, Sundqvist, Mikael |
| Přispěvatelé: | Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics (Faculty of Engineering), Algebra, Analysis and Dynamical Systems, Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Matematik LTH, Algebra, analys och dynamiska system, Originator |
| Zdroj: | Duke Mathematical Journal. 174(2):313-353 |
| Témata: | Natural Sciences, Mathematical Sciences, Mathematical Analysis, Naturvetenskap, Matematik, Matematisk analys |
| Popis: | We study the Pauli operator in a 2-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower bound to obtain a new formula on the number of eigenvalues of the magnetic Neumann Laplacian in the semiclassical limit. Our approach relies on reduction to a boundary Dirac operator. We analyze this boundary operator in two different ways. The first approach uses Atiyah-Patodi-Singer (APS) index theory. The second approach relies on a conservation law for the Benjamin-Ono equation. |
| Přístupová URL adresa: | https://doi.org/10.1215/00127094-2024-0029 |
| Databáze: | SwePub |
Nájsť tento článok vo Web of Science | Abstrakt: | We study the Pauli operator in a 2-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower bound to obtain a new formula on the number of eigenvalues of the magnetic Neumann Laplacian in the semiclassical limit. Our approach relies on reduction to a boundary Dirac operator. We analyze this boundary operator in two different ways. The first approach uses Atiyah-Patodi-Singer (APS) index theory. The second approach relies on a conservation law for the Benjamin-Ono equation. |
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| ISSN: | 00127094 15477398 |
| DOI: | 10.1215/00127094-2024-0029 |