Two-time quantum transport and quantum diffusion
  Based on the nonequilibrium Green's function technique, a unified theory is developed that covers quantum transport and quantum diffusion in bulk semiconductors on the same footing. This approach, which is applicable to transport via extended and localized states, extends previous semi-phenomenological studies and puts them on a firm microscopic basis. The approach is sufficiently general and applies not only to well-studied quantum transport problems, but also to models, in which the Hamiltonian does not commute with the dipole operator. It is shown that, even for the unified treatment of quantum transport and quantum diffusion in homogeneous systems, all quasi-momenta of the carrier distribution function are present and fulfill their specific function. Particular emphasis is put on the double-time nature of quantum kinetics. To demonstrate the existence of robust macroscopic transport effects that have a true double-time character, a phononless steady-state current is identified that appears only beyond the generalized Kadanoff-Baym ansatz. 
P. Kleinert