%0 Journal Article
%J 45th IEEE Conference on Decision and Control (2007) 2471-2476
%D 2007
%T Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
%A Claudio Altafini
%X 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.
%B 45th IEEE Conference on Decision and Control (2007) 2471-2476
%G en_US
%U http://hdl.handle.net/1963/1729
%1 2422
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-30T13:15:57Z\\nNo. of bitstreams: 1\\nquant-ph0506268.pdf: 339036 bytes, checksum: 0deeffc30853814638abac71df2a136d (MD5)
%R 10.1109/CDC.2006.377774