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

Abstract

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 $\hslash \sim N^{-1/3}$, we prove convergence in the large $N$ limit to the appropriate Magnetic Thomas-Fermi type model with various strength scalings of the magnetic field.