Norm convergence of confined fermionic systems at zero temperature

Abstract

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.