Control design for quantum systems, 1/2

Adiabatic control of the Schrodinger equation via intersection of eigenvalues

In this talk we present a results on approximate controllability of the bilinear Schroedinger equation which relies on adiabatic techniques and the existence of conical inersection between the eigenvalues of the Hamiltonian. In particular, we focus on the geometry of conical intersections: we introduce the notions of ``conicity matrix'', that describes the behaviour of the eigenstates in a neighborhood of the intersection, and of ``non-mixing curves'', that is special curves, in the space of controls, that improve the precision of the adiabatic passage through the conical intersection.