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arXiv · 1510.01124

The semi-classical limit of large fermionic systems

Jan Philip Solovej·S{ø}ren Fournais·Mathieu Lewin
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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.

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Jan Philip Solovej, S{ø}ren Fournais, Mathieu Lewin. 2015-10-05. The semi-classical limit of large fermionic systems. https://arxiv.org/abs/1510.01124

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