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

Søren Fournais; Peter S. Madsen

doi:10.1007/s00023-019-00880-6

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

Søren Fournais^*, Peter S. Madsen

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

4 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Annales Henri Poincare
Volume	21
Issue number	5
Pages (from-to)	1401-1449
ISSN	1424-0637
DOIs	https://doi.org/10.1007/s00023-019-00880-6
Publication status	Published - 1 May 2020
Externally published	Yes

Bibliographical note

Funding Information:
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. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Funding Information:
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.

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

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abstract = "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.",

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AU - Madsen, Peter S.

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

Abstract

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