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.

中文翻译：

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均匀磁场中受限费米子系统的半经典极限

我们考虑\（{\ mathbb {R}} ^ 3 \）中的N个相互作用的费米子系统，该费米子受外部电势限制并且存在均匀磁场。相互作用的强度具有平均场缩放1 / Ñ。使用半经典参数\（\ hbar \ sim N ^ {-1/3} \），我们证明了在大N限制下，具有适当强度的磁场的适当托马斯-费米型磁性模型的收敛性。