Sharp trace asymptotics for a class of 2D-magnetic operators
Abstract
In this paper we prove a two-term asymptotic formula for for the spectral counting function for a 2D magnetic Schrödinger operator on a domain (with Dirichlet boundary conditions) in a semiclassical limit and with strong magnetic field. By scaling, this is equivalent to a thermodynamic limit of a 2D Fermi gas submitted to a constant external magnetic field. The original motivation comes from a paper by H. Kunz in which he studied, among other things, the boundary correction for the grand-canonical pressure and density of such a Fermi gas. Our main theorem yields a rigorous proof of the formulas announced by Kunz. Moreover, the same theorem provides several other results on the integrated density of states for operators of the type (−ih∇−μA)^2 in L^2(Ω) with Dirichlet boundary conditions.
Additional Information
(Submitted on 3 Aug 2011) H.C. acknowledges support from the Danish F.N.U. grant Mathematical Physics. S.F. was supported by the Lundbeck Foundation, the Danish Natural Science Research Council and by the European Research Council under the European Community's Seventh Framework Program (FP7/2007–2013)/ERC grant agreement 202859.Attached Files
Submitted - 1108.0777.pdf
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Additional details
- Eprint ID
- 77101
- Resolver ID
- CaltechAUTHORS:20170501-100604320
- Lundbeck Foundation
- Danish Natural Science Research Council
- European Research Council (ERC)
- 202859
- Created
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2017-05-01Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field