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.

References in corpus (5)

• The Ground States of Large Quantum Dots in Magnetic Fields
• On the maximal ionization of atoms in strong magnetic fields
• Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics
• Semi-classical limit of large fermionic systems at positive temperature
• A discrete density matrix theory for atoms in strong magnetic fields

Cited by in corpus (3)

• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Semiclassical limit for almost fermionic anyons
• Multiple Landau level filling for a mean field limit of 2D fermions