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Sharp trace asymptotics for a class of 2D-magnetic operators

Cornean, Horia D. and Fournais, Søren and Frank, Rupert L. and Helffer, Bernard (2011) Sharp trace asymptotics for a class of 2D-magnetic operators. . (Submitted)

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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.

Item Type:Report or Paper (Discussion Paper)
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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.
Funding AgencyGrant Number
Lundbeck FoundationUNSPECIFIED
Danish Natural Science Research CouncilUNSPECIFIED
European Research Council (ERC)202859
Record Number:CaltechAUTHORS:20170501-100604320
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77101
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 17:48
Last Modified:03 Oct 2019 17:53

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