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Description

I will survey main results (both at the rigorous and the nonrigorous level) and open questions on the strongly correlated limit of DFT, including: - the connection between Hohenberg-Kohn-Lieb-Levy constrained-search and minimization of the interaction energy over $|\Psi|^2$ (alias Kantorovich optimal transport) - the SCE (alias Monge) ansatz in the Kantorovich problem: where it works, where it fails - the new quasi-Monge ansatz [1] which - unlike the SCE ansatz - always yields the minimum Kantorovich cost, but whose data complexity scales linearly instead of exponentially with the number of particles/marginals - asymptotic and semi-empirical exchange-correlation functionals related to the strictly correlated limit - representability challenges. [1] G.Friesecke, D.Vögler, Breaking the curse of dimension in multi-marginal Kantorovich optimal transport on finite state spaces, SIAM J. Math. Analysis Vol. 50 No. 4, 3996-4019, 2018