The quantitative semi-classical limit of a large Fermi system at zero temperature

2025/05/30 by Esteban Felipe Molina Cardenas, Cárdenas, Esteban
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Theoretical and Computational Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.24706

Abstract

In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi theory. The main novelty of the present article is quantifying the convergence rate with respect to the semi-classical parameter. One of the main ingredients is a recent result on the validity of semi-classical commutator estimates satisfied by the Hartree theory. Singular potentials, up to the Coulomb interaction, are included.

Citations

• Derivation of Hartree-Fock Dynamics and Semiclassical Commutator Estimates for Fermions in a Magnetic Field
• Emergence of fermion-mediated interactions in Bose-Fermi mixtures
• Commutator Estimates and Quantitative Local Weyl's Law for Schrödinger Operators with Non-Smooth Potentials
• Norm convergence of confined fermionic systems at zero temperature
• Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials
• The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime
• Convergence of Levy-Lieb to Thomas-Fermi density functional
• Mean-field Evolution of Fermionic Mixed States

Related

• Norm convergence of confined fermionic systems at zero temperature
• From the Hartree equation to the Vlasov-Poisson system: strong convergence for a class of mixed states
• Convergence of Levy-Lieb to Thomas-Fermi density functional
• Hartree-Fock dynamics for weakly interacting fermions
• Classical Limit in Scalar QFT at High Temperature