For electrons on a quantum ring, the Lieb density functional converges to the strictly correlated electrons functional and its representing potential converges to a regular Kantorovich potential in the semiclassical limit, for pairwise interactions satisfying an extended Seidl conjecture.
Friesecke,Optimal transport—a comprehensive introduction to modeling, analysis, simulation, applications, Society for Industrial and Applied Mathematics, Philadelphia, (2025)
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Strictly correlated electrons in a quantum ring: from Kohn-Sham to Kantorovich potentials
For electrons on a quantum ring, the Lieb density functional converges to the strictly correlated electrons functional and its representing potential converges to a regular Kantorovich potential in the semiclassical limit, for pairwise interactions satisfying an extended Seidl conjecture.