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The strong interaction limit of DFT: what's known, what's new, what's open (REVIEW)

Banff International Research Station for Mathematical Innovation and Discovery

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

Mathematics; Partial differential equations; Quantum theory; Applied mathematics

video/mp4

Author affiliation: Technische Universitat Munich

2020-12-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76709

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/