TY - JOUR
T1 - Controllability of the discrete-spectrum Schrodinger equation driven by an external field
JF - Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349
Y1 - 2009
A1 - Thomas Chambrion
A1 - Paolo Mason
A1 - Mario Sigalotti
A1 - Ugo Boscain
AB - 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.
UR - http://hdl.handle.net/1963/2547
U1 - 1572
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - An estimation of the controllability time for single-input systems on compact Lie Groups
JF - ESAIM Control Optim. Calc. Var. 12 (2006) 409-441
Y1 - 2006
A1 - Andrei A. Agrachev
A1 - Thomas Chambrion
AB - 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.
UR - http://hdl.handle.net/1963/2135
U1 - 2108
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy
JF - Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990
Y1 - 2005
A1 - Ugo Boscain
A1 - Thomas Chambrion
A1 - GrĂ©goire Charlot
AB - 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.
UR - http://hdl.handle.net/1963/2259
U1 - 1988
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - On the K+P problem for a three-level quantum system: optimality implies resonance
JF - J.Dynam. Control Systems 8 (2002),no.4, 547
Y1 - 2002
A1 - Ugo Boscain
A1 - Thomas Chambrion
A1 - Jean-Paul Gauthier
PB - SISSA Library
UR - http://hdl.handle.net/1963/1601
U1 - 2517
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -