TY - JOUR
T1 - Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
JF - 45th IEEE Conference on Decision and Control (2007) 2471-2476
Y1 - 2007
A1 - Claudio Altafini
AB - In 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.
UR - http://hdl.handle.net/1963/1729
U1 - 2422
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -