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.
Santambrogio,Optimal transport for applied mathematicians, Progress in Nonlinear Differential Equations and their Applications87, Birkhäuser/Springer, Cham (2015)
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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.