Ngoc Nhi Nguyen
Published 2023-05-10Version 1
We study grand-canonical interacting fermionic systems in the mean-field regime, in a trapping potential. We provide the first order term of integrated and pointwise Weyl laws, but in the case with interaction. More precisely, we prove the convergence of the densities of the grand-canonical Hartree-Fock ground state to the Thomas-Fermi ground state in the semiclassical limit $h\to 0$. For the proof, we write the grand-canonical version of the results of Fournais, Lewin and Solovej (Calc. Var. Partial Differ. Equ., 2018) and of Conlon (Commun. Math. Phys., 1983).
Two interacting particles on the half-line
On the Thomas-Fermi ground state in a harmonic potential
Supersymmetry and Models for Two Kinds of Interacting Particles
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