On the asymptotic number of edge states for magnetic Schrödinger operators
| dc.creator | Frank, Rupert L. | |
| dc.date | 2006-03-17 | |
| dc.date.accessioned | 2026-07-07T07:06:21Z | |
| dc.date.available | 2026-07-07T07:06:21Z | |
| dc.description | We consider a Schrödinger operator $(h\mathbf D -\mathbf A)^2$ with a positive magnetic field $B=\curl\mathbf A$ in a domain $Ω\subset\R^2$. The imposing of Neumann boundary conditions leads to spectrum below $h\inf B$. This is a boundary effect and it is related to the existence of edge states of the system. We show that the number of these eigenvalues, in the semi-classical limit $h\to 0$, is governed by a Weyl-type law and that it involves a symbol on $\partialΩ$. In the particular case of a constant magnetic field, the curvature plays a major role. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0603046 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0603046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109992 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the asymptotic number of edge states for magnetic Schrödinger operators | |
| dc.type | text |