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

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  • Horia D. Cornean, Aalborg University, Denmark
  • Søren Fournais
  • Rupert L. Frank, Princeton University, Unknown
  • Bernard Helffer, Universite Paris-Sud, France

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.

Original languageEnglish
JournalAnnales de l'Institut Fourier
Pages (from-to)2457-2513
Number of pages57
Publication statusPublished - 2013

    Research areas

  • Semiclassical asymptotics, Weyl law, magnetic Schrodinger operators, MAGNETIC SCHRODINGER-OPERATORS, LOCAL RIESZ MEANS, PAULI OPERATOR, EDGE STATES, FIELDS, BOTTLES, ENERGY

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