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In this paper we prove a two-term asymptotic formula for the spectral counting function for a D 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 D 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...
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