Memory effects and nonequilibrium transport in open many-particle quantum systems.
Full understanding of the relaxation mechanisms and far-from-equilibrium transport in modern mesoscopic structures requires that such systems be treated as open. We therefore generalize some of the core elements of the Kadanoff-Baym-Keldysh nonequilibrium Green's function formalism, inherently formulated for closed systems, to treatment of an open system, coupled with its environment. We define the two-time correlation functions and analyze the influence of the memory effects on the open-system transport. In the transient regime, the two-time correlation functions clearly show four distinct terms: a closed-system-like term, an entanglement term, and two memory terms that depend explicitly on the initial state of the environment. We show that it is not possible to completely eliminate the influence of the environment by a fortunate choice of the initial state, and approximating the system as closed is valid only in the limit of negligible system-environment coupling, which is never the case in the transient regime. We derive the transport equations for transients that properly account for the system-environment coupling. On the other hand, we address the important issue of transport in a far-from-equilibrium steady state. We show that, once a steady state is reached, the balance between the driving and relaxation forces implies that the two-time correlation functions regain a closed-system-like form, but with an effective, modified system Hamiltonian, and with the system statistical operator unrelated to that of the initial state. We emphasize that the difference between the transient and the far-from-equilibrium steady-state regimes, crucial for theoretical investigation of nonequilibrium quasiparticle transport, effectively lies within the different relative magnitude of the combined entanglement and memory terms with respect to the closed-system-like term in two-time correlation functions.