  We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum
Boltzmann equation, with the classical Maxwell distribution replaced by
Fermi-Dirac functions. To accommodate the spin density matrix, the distribution
functions become 2 x 2 matrix-valued. From an analytic perspective, the
efficient, commonly used BGK approximation of the collision operator is valid
in the present setting. The numerical scheme could leverage the principles of
LBM for simulating complex spin systems, with applications to spintronics.
