The semi-classical limit of large fermionic systems

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 prov...

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Published in:arXiv.org 2019-05
Main Authors: Solovej, Jan Philip, S{ø}ren Fournais, Lewin, Mathieu
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Lewin, Mathieu
description 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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Fermions
title The semi-classical limit of large fermionic systems
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