Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields.

We consider a system of N interacting fermions in 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 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. [ABSTRACT FROM AUTHOR]