Density Functional Theory for two-dimensional homogeneous materials
Mathematical Physics
2021-12-24 v2 Analysis of PDEs
math.MP
Abstract
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 provide some properties for the minimizer.
Cite
@article{arxiv.2102.12987,
title = {Density Functional Theory for two-dimensional homogeneous materials},
author = {David Gontier and Salma Lahbabi and Abdallah Maichine},
journal= {arXiv preprint arXiv:2102.12987},
year = {2021}
}