01194nas a2200097   4500008004300000245010500043210006900148520082100217100002201038856003601060       2007                        en_Ud  00aFeedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds0 aFeedback stabilization of quantum ensembles a global convergence3 aIn an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.1 aAltafini, Claudio  uhttp://hdl.handle.net/1963/1729