  Using the superfield nonequilibrium Greens function technique, we derive the
spatio-temporal spin magnetization quantum transport equations (SMQTEs) for a
two-band model of semiconductors. The relevant variables are the real
(Pauli-Dirac) spin, pseudo-spin, and the total charge. The results show that
the multi-band real SMQTEs are coupled to the pseudo-spin magnetization
transport equations by virtue of the presence of two additional discrete
quantum labels besides the up and down real-spin indices, namely, the
conduction and valence band quantum labels. The SMQTEs essentially consist of
three group of terms describing the rate of change, namely, (1) a group of
terms similar to the equation for particle quantum transport, i.e., with
spin-independent transport parameters, (2) a group of terms describing various
torques influencing the spin orientation and directional flow of spin
magnetization correlations or phase-space magnetization density, and (3) a
group of terms expressing the coupling of the real spin magnetization with the
pseudo-spin magnetization. Self-consistently, the pseudo-spin magnetization
equations incorporate the pseudo-spin/real spin coupling, as well as the
pseudo-spin coupling to the total charge.
