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The quantitative semi-classical limit of a large Fermi system at zero temperature
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The quantitative semi-classical limit of a large Fermi system at zero temperature
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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.
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Semi-classical limit of an attractive Fermi gas in one or two dimensions
For trapped attractive Fermi gases in 1D and 2D, as N grows the ground-state energy approaches the Thomas-Fermi energy, and ground states converge via Husimi functions.
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