Existence of minimizers for Kohn-Sham within the Local Spin Density Approximation

David Gontier (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS

The purpose of this article is to extend the work by Anantharaman and Cancès [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques.

Domaines: Physique mathématique [math-ph]

David Gontier. Existence of minimizers for Kohn-Sham within the Local Spin Density Approximation. Nonlinearity, 2014, 28 (1), pp.57-76. ⟨10.1088/0951-7715/28/1/57⟩. ⟨hal-01089108⟩