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.
Categories: math-ph math.MP math.SP