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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...
In a recent paper we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrodinger equation on a fixed domain. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrodinger operator. The aim of this presentation is to show that these conditions are generic with respect to the uncontrolled...
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...
We state an approximate controllability result for the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. This result applies both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. In addition we get some controllability properties for the density matrix. Finally we show, by means...
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