Quantum transport for a many-body system

We treat the quantum transport of an interacting system of electrons, impurities and phonons. The dynamic system is in a time-dependent electric field. We analyzed quantum transport process by using the quantum generalized Langevin equation, in which the system is shown to be equivalent to a quantum particle in a heat bath. After eliminating the heat-bath variables, the equation of motion for the quantum particle is written in a form of quantum generalized Langevin equation, with a memory term which reflects the retarded effects of the heat bath on the quantum particle.