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

Nonequilibrium Multi-Band Spin Quantum Transport Equations: Spin, Pseudo-Spin, and Total Charge Coupling