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Semi-classical limit of confined fermionic systems in homogeneous magnetic fields

We consider a system of $ N $ interacting fermions in $ \mathbb{R}^3 $ 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 $ \hbar \sim 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.