  A quantum kinetic theory of the spin transfer between carriers and Mn atoms
in a Mn doped diluted magnetic semiconductor is presented. It turns out that
the typical memory time associated with these processes is orders of magnitude
shorter than the time scale of the spin transfer. Nevertheless, Markovian rate
equations, which are obtained by neglecting the memory, work well only for bulk
systems. For quantum wells and wires the quantum kinetic results qualitatively
deviate from the Markovian limit under certain conditions. Instead of a
monotonic decay of an initially prepared excess electron spin, an overshoot or
even coherent oscillations are found. It is demonstrated that these features
are caused by energetic redistributions of the carriers due to the energy-time
uncertainty.
