The semi-classical limit of large fermionic systems
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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.
Original language | English |
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Article number | 105 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 57 |
Issue number | 4 |
ISSN | 0944-2669 |
DOIs | |
Publication status | Published - 2018 |
Links
- https://arxiv.org/pdf/1510.01124.pdf
Accepted author manuscript
ID: 152935146