Davies maps for qubits and qutrits

We investigate the dynamics of an N-level quantum system weakly coupled to a thermal reservoir. For any fixed temperature of the bath there exists a natural reference state: the equilibrium state of the system. Among all quantum operations on the system one distinguishes Davies maps, they preserve the equilibrium state, satisfy the detailed balance condition and belong to a semi-group. A complete characterization of the three-dimensional set of qubit Davies maps is given. We analyze these maps and find their minimum output entropy. A characterization of Davies maps for qutrits is also provided.