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

## TL;DR

This paper investigates the large particle limit of confined fermionic systems under homogeneous magnetic fields, establishing convergence to a Magnetic Thomas-Fermi model with semi-classical analysis.

## Contribution

It rigorously derives the semi-classical limit of interacting fermions in magnetic fields, extending the Thomas-Fermi theory to include magnetic effects with various field strengths.

## Key findings

- Convergence to Magnetic Thomas-Fermi model in large N limit
- Semi-classical parameter scales as N^{-1/3}
- Results applicable to different magnetic field strengths

## 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 $ \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.