01061nas a2200133   4500008004300000245009500043210006900138520060700207100002200814700001700836700002100853700001700874856003600891       2009                        en_Ud  00aControllability of the discrete-spectrum  Schrodinger equation driven by an external field0 aControllability of the discretespectrum Schrodinger equation dri3 aWe prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.1 aChambrion, Thomas1 aMason, Paolo1 aSigalotti, Mario1 aBoscain, Ugo  uhttp://hdl.handle.net/1963/254700974nas a2200109   4500008004300000245009300043210006900136520057600205100002500781700002200806856003600828       2006                        en_Ud  00aAn estimation of the controllability time for single-input systems on compact Lie Groups0 aestimation of the controllability time for singleinput systems o3 aGeometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper.1 aAgrachev, Andrei, A.1 aChambrion, Thomas  uhttp://hdl.handle.net/1963/213501293nas a2200121   4500008004300000245009700043210006900140520086400209100001701073700002201090700002301112856003601135       2005                        en_Ud  00aNonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy0 aNonisotropic 3level quantum systems complete solutions for minim3 aWe apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.1 aBoscain, Ugo1 aChambrion, Thomas1 aCharlot, Grégoire  uhttp://hdl.handle.net/1963/225900435nas a2200121   4500008004100000245008600041210006900127260001800196100001700214700002200231700002400253856003600277       2002                        en  d00aOn the K+P problem for a three-level quantum system: optimality implies resonance0 aKP problem for a threelevel quantum system optimality implies re  bSISSA Library1 aBoscain, Ugo1 aChambrion, Thomas1 aGauthier, Jean-Paul  uhttp://hdl.handle.net/1963/1601