Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on January 31, 2007
Proceedings of the London Mathematical Society 2007 95(1):1-19; doi:10.1112/plms/pdl024
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
95/1/1    most recent
pdl024v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Frank, R. L.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

On the asymptotic number of edge states for magnetic Schrödinger operators

Rupert L. Frank

Royal Institute of Technology
Department of Mathematics 100 44 Stockholm
Sweden
rupert{at}math.kth.se

We consider a Schrödinger operator (hD – A)2 with a positive magnetic field B = curlA in a domain {Omega} sub R2. The imposing of Neumann boundary conditions leads to the existence of some spectrum below h isin 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 {partial}{Omega}. In the particular case of a constant magnetic field, the curvature plays a major role.

2000 Mathematics Subject Classification 35P20, 35J10.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.