Journal of Statistical Physics, Vol. 114, Nos. 1/2, January 2004. p. 361-453.
We investigate the ensemble averaged evolution of N-electron systems dynamically coupled to a statistical environment. The electrons are characterized by their spatial and by their spin properties. While the Hilbert space for single electrons is given by the tensor product of the Hilbert spaces associated with both properties, the corresponding Hilbert space for N-electron systems cannot be factorized. Consequently, quantum correlations between spatial and spin properties become extremely important. We assume that the evolution of the spin properties is controlled by spin-orbit interaction and that the spatial properties take the part of a bath held near some equilibrium. This description is appropriate for magnetic systems where the electronic states near the ground state correspond to different spin configurations, whereas electronic states with large excitation energies belong to different spatial-orbital configurations. In order to determine the coarse grained evolution of the spin properties, we have to know the evolution of the N-electron system over time intervals larger than the bath-correlation time. This is obtained from the first- and second-order contributions in the interaction picture. We show that, in spite of the strong quantum correlations between spin properties and spatial properties, the coarse grained statistical evolution of the electronic spin properties may be described by a set of coupled master equations.