The semi-classical limit of ground states of large systems of fermions was studied by Fournais et al. (Calc Var Partial Differ Equ 57:105, 2018). In particular, the authors prove weak convergence toward classical states associated with the minimizers of the Thomas–Fermi functional. In this paper, we revisit this limit and show that under additional assumptions—and, using simple arguments—it is possible to prove that strong convergence holds in relevant normed spaces.

中文翻译：

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零温约束费米子系统的范数收敛

Fournais 等人研究了大型费米子系统基态的半经典极限。（计算 Var 偏微分方程 57:105，2018）。特别是，作者证明了与托马斯-费米泛函的极小值相关的经典态的收敛性较弱。在本文中，我们重新审视这个极限，并表明在额外的假设下——并且使用简单的论证——可以证明强收敛性在相关的规范空间中成立。