Counting Negative Eigenvalues for the Magnetic Pauli Operator

Autor:	Fournais, Søren, Frank, Rupert L., Goffeng, Magnus, Kachmar, Ayman, Sundqvist, Mikael
Rok vydání:	2023
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Differential Geometry Mathematics - Functional Analysis 35P15 58J20 47A40
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
Externí odkaz:	http://arxiv.org/abs/2307.16079 Zobrazit plný text záznamu View this record from Arxiv