  We study a single Markovian qubit governed by a Lindblad master equation and
subject to fast unitary control. Using reduced control systems and optimal
control theory we determine (i) controls for cooling and heating such systems
in a time-optimal way as well as (ii) the set of stabilizable states in the
Bloch ball. No restrictions on the Lindblad equation are assumed, and several
known results, for instance for the Bloch equations, are recovered. Furthermore
we introduce integral systems, for which the solutions take a particularly nice
form. These integral systems include all systems with real Lindblad terms as
well as all coolable systems. The method allows for intuitive visualizations
and is mostly analytical, making use of only basic numerical methods.
