%0 Journal Article
%J Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349
%D 2009
%T Controllability of the discrete-spectrum Schrodinger equation driven by an external field
%A Thomas Chambrion
%A Paolo Mason
%A Mario Sigalotti
%A Ugo Boscain
%X We 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.
%B Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349
%G en_US
%U http://hdl.handle.net/1963/2547
%1 1572
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:32:19Z\\nNo. of bitstreams: 1\\n2008-ttinger.pdf: 270196 bytes, checksum: e706dbae08d996576cefe55f53d7284e (MD5)
%R 10.1016/j.anihpc.2008.05.001
%0 Journal Article
%J ESAIM Control Optim. Calc. Var. 12 (2006) 409-441
%D 2006
%T An estimation of the controllability time for single-input systems on compact Lie Groups
%A Andrei A. Agrachev
%A Thomas Chambrion
%X Geometric 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.
%B ESAIM Control Optim. Calc. Var. 12 (2006) 409-441
%G en_US
%U http://hdl.handle.net/1963/2135
%1 2108
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-24T13:09:42Z\\nNo. of bitstreams: 1\\ncocv0452.pdf: 441157 bytes, checksum: 7c8ead7c835051e17567fe9bb8a60fbe (MD5)
%R 10.1051/cocv:2006007
%0 Journal Article
%J Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990
%D 2005
%T Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy
%A Ugo Boscain
%A Thomas Chambrion
%A GrĂ©goire Charlot
%X We 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.
%B Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990
%G en_US
%U http://hdl.handle.net/1963/2259
%1 1988
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:55:27Z\\nNo. of bitstreams: 1\\n0409022v2.pdf: 578605 bytes, checksum: db7298996e781c3a8546c3d01ee28384 (MD5)
%0 Journal Article
%J J.Dynam. Control Systems 8 (2002),no.4, 547
%D 2002
%T On the K+P problem for a three-level quantum system: optimality implies resonance
%A Ugo Boscain
%A Thomas Chambrion
%A Jean-Paul Gauthier
%B J.Dynam. Control Systems 8 (2002),no.4, 547
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/1601
%1 2517
%2 Mathematics
%3 Functional Analysis and Applications
%$ Made available in DSpace on 2004-09-01T13:05:08Z (GMT). No. of bitstreams: 1\\nmath.OC0204233.pdf: 252630 bytes, checksum: 14283368a7848e46caf6447b4bad85d4 (MD5)\\n Previous issue date: 2002
%R 10.1023/A:1020767419671