Nonequilibrium Spin Magnetization Quantum Transport Equations: Spin and   Charge Coupling
  The classical Bloch equations of spin magnetization transport is extended to fully time-dependent and highly-nonlinear nonequilibrium spin magnetization quantum distribution function transport (SMQDFT) equations. The relevant variables are the spinor correlation functions which separate into charge and spin magnetization distributions that becomes highly coupled in SMQDFT equa- tions. The leading terms consist of the Boltzmann kinetic equation with spin-orbit coupling in a magnetic eld together with spin-dependent scattering terms which contribute to the torque. These do not have analogue within the classical relaxation-dephasing picture, but are inherently quantum many-body effects. These should incorporate the spatiotemporal-dependent phase-space dynam- ics of Elliot-Yafet and Dyakonov-Perel scatterings. The resulting SMQDFT equations should serve as a theoretical foundation for computational spintronic and nanomagnetic device applications, in ultrafast-switching-speed/low-power performance and reliability analyses. 
F. A. Buot, R. A. Loberternos, R. E. S. Otadoy, and D. L. Villarin
quant-ph cond-mat.mes-hall