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- Title
On the asymptotic number of edge states for magnetic Schrodinger operators.
- Abstract
We consider a Schrödinger operator (hD - A)2 with a positive magnetic field B = curlA in a domain O ? ℝ2. The imposing of Neumann boundary conditions leads to the existence of some spectrum below h ? f 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 ? 0, is governed by a Weyl-type law and that it involves a symbol on ?O. In the particular case of a constant magnetic field, the curvature plays a major role.
- Subjects
SCHRODINGER operator; MAGNETIC fields; NEUMANN problem; EIGENVALUES; WEYL theory of boundary value problems; CURVATURE
- Publication
Proceedings of the London Mathematical Society, 2007, Vol 95, Issue 1, p1
- ISSN
0024-6115
- Publication type
Article
- DOI
10.1112/plms/pdl024