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.
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Acknowledgements
I am grateful to J.K Miller and N. Pavlović for discussions that ultimately led to the study of the problem in this article. I am also very thankful to D. Hundertmark for his comments that helped improve an earlier version of this manuscript. I would also like to acknowledge important remarks from two anonymous referees that helped significantly improve the conclusion of Theorem 1, covering now the additional range \( p \in (2, \infty )\). The author gratefully acknowledges support from the Provost’s Graduate Excellence Fellowship at The University of Texas at Austin and from the NSF Grant DMS-2009549, and the NSF Grant DMS-2009800 through T. Chen.
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Cárdenas, E. Norm convergence of confined fermionic systems at zero temperature. Lett Math Phys 114, 38 (2024). https://doi.org/10.1007/s11005-024-01785-0
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DOI: https://doi.org/10.1007/s11005-024-01785-0