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The strictly-correlated electron functional for spherically symmetric systems revisited

Seidl, Michael; Marino, Simone; Gerolin, Augusto; Nenna, Luca; Giesbertz, Klaas; Gori-Giorgi, Paola (2017), The strictly-correlated electron functional for spherically symmetric systems revisited. https://basepub.dauphine.fr/handle/123456789/17198

Type
Document de travail / Working paper
External document link
https://hal.inria.fr/hal-01469822
Date
2017
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
23
Metadata
Show full item record
Author(s)
Seidl, Michael
Marino, Simone
Gerolin, Augusto
Nenna, Luca
Giesbertz, Klaas
Gori-Giorgi, Paola
Abstract (EN)
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys. Rev. A 75, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math. Models Methods Appl. Sci., 26 1025 (2016)] have recently shown that these conjectured maps are not always optimal. Here we revisit the whole issue both from the formal and numerical point of view, finding that even if the conjectured maps are not always optimal, they still yield an interaction energy (cost) that is numerically very close to the true minimum. We also prove that the functional built from the conjectured maps has the expected functional derivative also when they are not optimal.
Subjects / Keywords
Hohenberg-Kohn functional

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