The semi-classical limit of large fermionic systems

Abstract

We study a system of $N$ fermions in the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hslash =N^{-1/d}$ where $d$ is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas-Fermi minimizers in the limit $N\to \infty$. The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti-Hewitt-Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.

Final version published in Calculus of Variations and Partial Differential Equations (2018)

References in corpus (3)

• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• Geometric methods for nonlinear many-body quantum systems
• From the Hartree dynamics to the Vlasov equation

Cited by in corpus (2)

• Statistical Mechanics of the Uniform Electron Gas
• Stability of the Laughlin phase against long-range interactions