On the control of quantum statistical systems

The problem of preparing a system in some initial configuration is discussed for quantum statistical systems whose dynamics are generated by Markovian semigroups. The system is regulated by a set of controls and the central problem is to determine how the controls should be varied in order to bring the system as close as possible to the desired configuration in a fixed finite time. General equations are derived which allow one to determine how the controls should be regulated. The application of the result to a simple system is outlined.