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.
Originalsprog | Engelsk |
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Artikelnummer | 105 |
Tidsskrift | Calculus of Variations and Partial Differential Equations |
Vol/bind | 57 |
Udgave nummer | 4 |
ISSN | 0944-2669 |
DOI | |
Status | Udgivet - 2018 |