Approximate controllability by adiabatic methods of the Schrödinger equation with nonlinear Hamiltonian.
Résumé
We consider quantum systems described by a controlled Schrödinger equation, where the Hamiltonian dependssmoothly on three external inputs. We use adiabatic techniquesto provide a constructive controllability result in some portionof the discrete spectrum, provided that it is conically connected.The case of Schrödinger Hamiltonians with electromagneticfields fits the nonlinear setting studied in this paper.