Counting Negative Eigenvalues for the Magnetic Pauli Operator
Autor: | Fournais, Søren, Frank, Rupert L., Goffeng, Magnus, Kachmar, Ayman, Sundqvist, Mikael |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We study the Pauli operator in a two-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 semi-classical 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 index theory. The second approach relies on a conservation law for the Benjamin-Ono equation. Comment: 29 pages, 1 figure |
Databáze: | arXiv |
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