2011/08/03 by Horia D. Cornean, Cornean, Horia D., Soren Fournais +5
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP
paper · pdf · doi:10.48550/arxiv.1108.0777
arxiv created 2011/08/03 · arxiv updated 2011/08/04
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∇- μ\bf A)2 in L2(Ω) with Dirichlet boundary conditions.