A bilinear optimal control problem applied to a time dependent Hartree--Fock equation coupled with classical nuclear dynamics

Lucie Baudouin

Abstract: We study a problem of bilinear optimal control for the electronic wave function of an Helium atom by an external time dependent electric field. The behavior of the atom is modeled by the Hartree--Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, corresponding to the motion of the nucleus. We prove the existence of a bilinear optimal control in the case when the position of the nucleus is known and also prove the corresponding optimality condition. Then, we detail the proof of the existence of an optimal control for the coupled system and complete the study giving a formal optimality condition to define the electric control.

Keywords: Hartree--Fock equation; optimal control; optimality condition.

Classification (MSC2000): 49J20, 35Q55.

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