Introduction to mathematical density-functional theory
The quantum-mechanical description of interacting electrons can be tackled using the one-body particle density. We have recently reviewed the theoretical foundation of density-functional theory (DFT) with focus on a rigorous mathematical formulation [1]. In addition, a rather novel ingredient of DFT is Moreau-Yosida regularization, which we have just now connected to the Kohn-Sham approach (the workhorse of DFT) to obtain «nature’s glue» as a limit procedure [2].
[1] M. Penz, E. I. Tellgren, M. A. Csirik, M. Ruggenthaler, and A. Laestadius https://arxiv.org/pdf/2211.16627.pdf (2022)
[2] M. Penz, M. A. Csirik, and A. Laestadius, https://arxiv.org/pdf/2212.12727.pdf (2022)