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

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  • Horia D. Cornean, Aalborg Universitet, Danmark
  • Søren Fournais
  • Rupert L. Frank, Princeton Univ, Princeton University, Dept Math, Ukendt
  • Bernard Helffer, Universite Paris-Sud, Frankrig

In this paper we prove a two-term asymptotic formula for the spectral counting function for a 2D magnetic Schrodinger 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 del - mu A)(2) in L-2(Omega) with Dirichlet boundary conditions.

OriginalsprogEngelsk
TidsskriftAnnales de l'Institut Fourier
Vol/bind63
Nummer6
Sider (fra-til)2457-2513
Antal sider57
ISSN0373-0956
DOI
StatusUdgivet - 2013

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