Summary: Controllability and simultaneous controllability of
isospectral bilinear control systems on complex flag
SISSA-ISAS, International School for Advanced Studies
via Beirut 2-4, 34014 Trieste, Italy,
tel. +39 040 3787431, fax + 39 040 3787528
October 24, 2008
For isospectral bilinear control systems evolving on the so-called complex flag man-
ifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action)
it is shown that controllability is almost always verified. Easy and generic sufficient
conditions are provided. The result applies to the problem of density operator con-
trollability of finite dimensional quantum mechanical systems. In addition, we show
that systems having different drifts (corresponding for example to different Larmor
frequencies) are simultaneously controllable by the same control field.
keyword Controllability, Simultaneous controllability, Bilinear control systems, Isospec-
tral evolution, Quantum control.
The conjugation action of the unitary group over the vector space of Hermitian matrices