Published July 2007
| Submitted
Journal Article
Open
On the asymptotic number of edge states for magnetic Schrödinger operators
- Creators
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Frank, Rupert L.
Abstract
We consider a Schrödinger operator ( hD − A )^2 with a positive magnetic field B = curlA in a domain Ω ⊂ ℝ^2 . 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 ∂Ω. In the particular case of a constant magnetic field, the curvature plays a major role.
Additional Information
© 2007 London Mathematical Society. Received 17 March 2006; revised 4 July 2006; published online 31 January 2007. The author wishes to thank Professor B. Helffer for the invitation to Orsay and numerous fruitful discussions. He is also grateful to S. Fournais and A. Hansson for useful remarks. Financial support through the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT) as well as through the European Research Network 'Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems' (Contract Number HPRN-CT-2002-00277) is gratefully acknowledged.Attached Files
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Additional details
- Eprint ID
- 77879
- Resolver ID
- CaltechAUTHORS:20170601-081138045
- European Science Foundation
- HPRN-CT-2002-00277
- European Union Network Project
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2017-06-01Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field