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In this paper we consider the problem of inducing a transition in a controlled quantum mechanical system whose spectrum loses simplicity for some values of the control. We study the situation in which the Hamiltonian of the system is real, and we are in presence of two controls. In this case, eigenvalue crossings are generically conical. Adiabatic approximation is used to decouple a finite dimensional...
We consider a non-resonant system of finitely many bilinear Schrodinger equations with discrete spectrum driven by the same scalar control. We prove that this system can approximately track any given system of trajectories of density matrices, up to the phase of the coordinates. The result is valid both for bounded and unbounded Schrodinger operators. The method used relies on finite-dimensional control...
We consider the simplest model for controlling the rotation of a molecule by the action of an electric field, namely a quantum planar pendulum. This problem consists in characterizing the controllability of a PDE (the Schrodinger equation) on a manifold with nontrivial topology (the circle S1). The drift has discrete spectrum and its eigenfunctions are trigonometric functions. Some controllability...
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