Study of transients in the electron quantum transport by nonequilibrium Green's function often requires an explicit inclusion of correlations at a finite initial time. For processes embedded in a host process, a universal treatment of the correlated initial conditions based on the formalism of partitioning in time allows to express their self-energy including the ``irregular'' correlation part in terms of the known properties of the host process. This unified formalism also yields the renormalized semigroup property for propagators and the reconstruction equations for the particle correlation function. The Bogolyubov principle of the decay of correlations then permits to buildup a theory of quantum transport equations with finite-time initial conditions.
Study of transients in the electron quantum transport by nonequilibrium Green's function often requires an explicit inclusion of correlations at a finite initial time. For processes embedded in a host process, a universal treatment of the correlated initial conditions based on the formalism of partitioning in time allows to express their self-energy including the ``irregular'' correlation part in terms of the known properties of the host process. This unified formalism also yields the renormalized semigroup property for propagators and the reconstruction equations for the particle correlation function. The Bogolyubov principle of the decay of correlations then permits to buildup a theory of quantum transport equations with finite-time initial conditions.
Construction of the electron quantum transport equations from Non-Equilibrium Green's Functions is presently based on Reconstruction Theorems, reducing full description of a non-equilibrium system to a dynamic theory in terms of one-particle quantities. This approach, stemming from the original Kadanoff-Baym Ansatz, and based on a suitably renormalized NGF formalism, can be brought to a close parallel with the Time Dependent Density Functional Theory. This concerns, in particular, the role of correlations at a finite initial time. A universal treatment of these initial conditions is possible for the switch-on states, while more general initial states have so far to be treated individually.
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.
In a nonequilibrium system, quasiparticles are defined, consistently with the construction of quantum transport equations, as one-electron excitations whose propagator possesses a time-local optical potential. This potential is constructed as a solution of the phase equation, a self-consistency condition reducing the renormalized Dyson equation to a formerly proposed multiplicative composition rule for the propagators. The Dyson equation for the particle correlation function is transformed to a renormalized quasiparticle reconstruction equation, whose leading term represents the quasiparticle Kadanoff-Baym ansatz [Physica E 29, 196 (2005)], an improvement over the standard generalized Kadanoff-Baym ansatz.
We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems ( Phys. Rev. Lett. , 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.
Abstract We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green’s function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive—encompassing pump–probe scenarios as well as driven quantum systems—we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron–phonon couplings, topological superconductors, and optically responsive molecular junctions where electron–photon couplings are relevant.
This review deals with the state of the art and perspectives of description of nonequilibrium many-body systems using the nonequilibrium Green's function (NGF) method. The basic aim is to describe time evolution of the many-body system from its initial state over its transient dynamics to its long time asymptotic evolution. First, we discuss basic aims of transport theories to motivate the introduction of the NGF techniques. Second, this article summarizes the present view on construction of the electron transport equations formulated within the NGF approach to nonequilibrium. We discuss incorporation of complex initial conditions to the NGF formalism, and the NGF reconstruction theorem, which serves as a tool to derive simplified kinetic equations. Three stages of evolution of the nonequilibrium, the first described by the full NGF description, the second by a non-Markovian generalized master equation and the third by a Markovian master equation will be related to each other.