  We study open quantum systems whose evolution is governed by a master
equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a
characterization of the convex set of steady states of such systems based on
the generalized Bloch representation. It is shown that an isolated steady state
of the Bloch equation cannot be a center, i.e., that the existence of a unique
steady state implies attractivity and global asymptotic stability. Necessary
and sufficient conditions for the existence of a unique steady state are
derived and applied to different physical models including two- and four-level
atoms, (truncated) harmonic oscillators, composite and decomposable systems. It
is shown how these criteria could be exploited in principle for quantum
reservoir engineeing via coherent control and direct feedback to stabilize the
system to a desired steady state. We also discuss the question of limit points
of the dynamics. Despite the non-existence of isolated centers, open quantum
systems can have nontrivial invariant sets. These invariant sets are center
manifolds that arise when the Bloch superoperator has purely imaginary
eigenvalues and are closely related to decoherence-free subspaces.
