On some periodic Hartree-type models for crystals

Isabelle Catto (1) , Claude Le Bris (2) , Pierre Louis Lions (1, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
3 Collège de France - Chaire Équations aux dérivées partielles et applications

We continue here our study of the thermodynamic limit for various models of Quantum Chemistry. More specifically, we study the Hartree and the restricted Hartree model. For the restricted Hartree model, we prove the existence of the thermodynamic limit for the energy per unit volume. We also define a periodic problem associated to the Hartree model, and we prove that it is well-posed.

Domaines: Equations aux dérivées partielles [math.AP]

Isabelle Catto, Claude Le Bris, Pierre Louis Lions. On some periodic Hartree-type models for crystals. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2002, 19 (2), pp.143-190. ⟨hal-00157675⟩