Density Functional Theory for two-dimensional homogeneous materials
Gontier, David; Lahbabi, Salma; Maichine, Abdallah (2021), Density Functional Theory for two-dimensional homogeneous materials, Communications in Mathematical Physics, 388, p. 1475–1505. 10.1007/s00220-021-04240-6
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Mathematical Physics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ecole Nationale Supérieure d'Electricité et de Mécanique [Casablanca] [ENSEM]
Abstract (EN)We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced equations in the remaining directions. In the Thomas–Fermi model, we prove that there is perfect screening, and provide decay estimates for the electronic density away from the slab. In Kohn–Sham models, we prove that the Pauli principle is replaced by a penalization term in the energy. In the reduced Hartree–Fock model in particular, we prove that the resulting model is well-posed, and give some properties of the minimizer.
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