  We systematically derive a linear quantum collision operator for the
spinorial Wigner transport equation from the dynamics of a composite quantum
system. For suitable two particle interaction potentials, the particular matrix
form of the collision operator describes spin decoherence or even spin
depolarization as well as relaxation towards a certain momentum distribution in
the long time limit. It is demonstrated that in the semiclassical limit the
spinorial Wigner equation gives rise to several semiclassical spin-transport
models. As an example, we derive the Bloch equations as well as the spinorial
Boltzmann equation, which in turn gives rise to spin drift-diffusion models
which are increasingly used to describe spin-polarized transport in spintronic
devices. The presented derivation allows to systematically incorporate
Born-Markov as well as quantum corrections into these models.
