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

Fournais, Søren; Madsen, Peter (2020), Semi-classical Limit of Confined Fermionic Systems in Homogeneous Magnetic Fields, Annales Henri Poincaré, 21, 5, p. 1401-1449. 10.1007/s00023-019-00880-6

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Annales Henri Poincaré
Volume
21
Number
5
Publisher
Springer
Pages
1401-1449
Publication identifier
Metadata
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Author(s)
Fournais, Søren
Aarhus University
Madsen, Peter
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider a system of N interacting fermions in R3 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 ℏ∼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.
Subjects / Keywords
Spectral theory; semi-classical analysis; mean-field limits; fermionicsystems; magnetic fields