Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields
Résumé
We consider a system of N interacting fermions in R3 confined by an external potential and in the presence of a homogeneous magnetic field. The intensity of the interaction has the mean-field scaling 1/N. With a semi-classical parameter ℏ∼N−1/3, we prove convergence in the large N limit to the appropriate Magnetic Thomas-Fermi type model with various strength scalings of the magnetic field.
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