The strictly-correlated electron functional for spherically symmetric systems revisited - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

The strictly-correlated electron functional for spherically symmetric systems revisited

Résumé

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.
Fichier principal
Vignette du fichier
SeiDiMGerNenGieGor.pdf (947.75 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01469822 , version 1 (16-02-2017)

Identifiants

  • HAL Id : hal-01469822 , version 1

Citer

Michael Seidl, Simone Di Marino, Augusto Gerolin, Luca Nenna, Klaas J H Giesbertz, et al.. The strictly-correlated electron functional for spherically symmetric systems revisited. 2017. ⟨hal-01469822⟩
601 Consultations
210 Téléchargements

Partager

Gmail Facebook X LinkedIn More