Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
22 October 2019 |
06 November 2019 |
10 March 2020 |
Abstract: In this talk, we present some results about the well-posedness of the reduced Hartree-Fock model with self-generated magnetic fields for molecules and crystals. In particular, we exhibit a critical value alpha_c > 0 such that, if the fine structure constant alpha is smaller than alpha_c, then the corresponding system is stable, whereas if alpha is greater than alpha_c, it is unstable. We give an explicit characterisation of alpha_c as a minimisation problem over the set of zero-modes, and we prove that the critical values for the molecular case and the periodic case coincide. Finally, we give some results about the existence of minimisers.
