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Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields

  • Søren FournaisEmail author
  • Peter S. Madsen
Article
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Abstract

We consider a system of N interacting fermions in \( {\mathbb {R}}^3 \) confined by an external potential and in the presence of a homogeneous magnetic field. The intensity of the interaction has the mean-field scaling 1/N. With a semi-classical parameter \( \hbar \sim N^{-1/3} \), we prove convergence in the large N limit to the appropriate magnetic Thomas–Fermi-type model with various strength scalings of the magnetic field.

Mathematics Subject Classification

Primary 81Q20 Secondary 35P20 

Notes

Acknowledgements

The authors were partially supported by the Sapere Aude Grant DFF–4181-00221 from the Independent Research Fund Denmark. Part of this work was carried out while both authors visited the Mittag-Leffler Institute in Stockholm, Sweden.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsAarhus UniversityAarhus CDenmark
  2. 2.CNRS & CEREMADEParis-Dauphine University, PSL UniversityParisFrance

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