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

Gontier, David; Lahbabi, Salma

Gontier, David; Lahbabi, Salma (2019), The reduced Hartree-Fock model with self-generated magnetic fields, Journal of Mathematical Physics, 60, 8. 10.1063/1.5100919

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Type

Article accepté pour publication ou publié

Date

2019

Journal name

Journal of Mathematical Physics

Volume

Number

Publisher

American Institute of Physics

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lahbabi, Salma
Ecole Nationale Supérieure d'Electricité et de Mécanique [Casablanca] [ENSEM]

Abstract (EN)

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 αc > 0 such that if the fine structure constant α is smaller than αc, then the corresponding system is stable, whereas if α is greater than αc, it is unstable. We give an explicit characterization of αc 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.

Subjects / Keywords

Density-matrix; Operator theory; Magnetic energy; Partial differential equations; Probability theory; Magnetic fields; Self consistent field methods