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The semi-classical limit of large fermionic systems

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  • Søren Fournais
  • Mathieu Lewin, CNRS University Paris-Dauphine
  • ,
  • Jan Philip Solovej, University of Copenhagen

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 ħ= 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→ ∞. 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 languageEnglish
Article number105
JournalCalculus of Variations and Partial Differential Equations
Number of pages42
Publication statusPublished - 1 Aug 2018

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