The reduced Hartree-Fock model with self-generated magnetic fields

摘要

We study the well-posedness of the reduced Hartree-Fock model for molecules and perfect crystals when taking into account a self-generated magnetic field. 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 characterization of alpha(c) as a minimization 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 prove the existence of minimizers when the system is neutral or positively charged.