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On the asymptotic number of edge states for magnetic Schrodinger operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2007 (English)In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 95, no 1, 1-19 p.Article in journal (Refereed) Published
Abstract [en]

We consider a Schrodinger operator (hD - A)(2) with a positive magnetic field B = curl A in a domain Omega subset of R-2. The imposing of Neumann boundary conditions leads to the existence of some 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 -> 0, is governed by a Weyl-type law and that it involves a symbol on partial derivative Omega. In the particular case of a constant magnetic field, the curvature plays a major role.

Place, publisher, year, edition, pages
2007. Vol. 95, no 1, 1-19 p.
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URN: urn:nbn:se:kth:diva-37010DOI: 10.1112/plms/pdl024ISI: 000247956200001ScopusID: 2-s2.0-52249110881OAI: diva2:431821
Available from: 2011-07-26 Created: 2011-07-26 Last updated: 2011-07-26Bibliographically approved

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Frank, Rupert L.
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