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Young Seminar
Organizers: Douglas Lundholm (IHP) & Julien Sabin (Cergy)


Antoine Levitt (Paris-Dauphine): "The multiconfiguration Dirac-Fock model"
Tuesday 07 May 2013, 14:00 - 15:00
Room 314


Abstract: We consider the N-body problem for an atomic or molecular system, in the Born-Oppenheimer approximation. Since this problem is too big to solve, approximation methods such as the Hartree-Fock model are routinely used to compute electronic properties of molecules or solids. We will examine a two-way generalization of this model, to the multiconfiguration (several Slater determinants) and relativistic (using the Dirac operator) case.


The Hartree-Fock model was studied rigorously by Lieb-Simon (1977) and Lions (1987), the Dirac-Fock model by Esteban-Séré (1999), and the multiconfiguration nonrelativistic model by Friesecke (2003) and Lewin (2004). The relativistic multiconfiguration case poses new mathematical issues : because of the properties of the Dirac operator, the equations involving orbitals with small occupation numbers only make sense when the speed of light is sufficiently large. After a presentation of the context and a review of previous works, I will sketch a proof of the existence of "ground states" for the multiconfiguration Dirac-Fock model, in the weakly relativistic regime.