The semi-classical limit of large fermionic systems

Søren Fournais, Mathieu Lewin, Jan Philip Solovej

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27 Citationer (Scopus)

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 $\hbar=N^{-1/d}$ 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.
OriginalsprogEngelsk
Artikelnummer105
TidsskriftCalculus of Variations and Partial Differential Equations
Vol/bind57
Udgave nummer4
ISSN0944-2669
DOI
StatusUdgivet - 2018

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