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.
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.
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.
This review deals with the state of the art and perspectives of description of nonequi-librium 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 Markovianmaster equation will be related to each other.
Within the Landauer approach to conduction discussed in the previous chapter, electron interactions have been included only at the mean-field level. This is quite a strong approximation, especially in nanojunctions, where large current densities are common. I therefore want to go beyond this level of description. I can follow two different routes. (1) I can develop a functional theory of quantum correlations via time-dependent effective single-particle equations, as I will do in Chapter 7 where I will use dynamical density-functional theories within the micro-canonical approach to conduction. (2) I can try to solve the time-dependent Schrödinger equation 1.16 – or its mixed-state version, the Liouville-von Neumann equation 1.60 – directly. Written this way, this last proposition seems hopeless. In reality, we can employ a many-body technique, known as the non-equilibrium Green's function formalism (NEGF), also referred to as the Keldysh formalism (Keldysh, 1964; Kadanoff and Baym, 1962), which allows us, at least in principle, to do just that: solve the time-dependent Schrödinger equation for an interacting many-body system exactly, from which one can, in principle, calculate the time-dependent current. This is done by solving equations of motion for specific time-dependent single-particle Green's functions, from which the physical properties of interest, such as the charge and current densities, can be obtained. I have stressed the term “time-dependent” several times, because, as I will show in a moment, the NEGF is “exact” only when one solves the time-dependent Schrödinger equation for a closed quantum system, subject to deterministic perturbations: the system is closed but not necessarily isolated. These perturbations may drive the system far away from its initial state of thermodynamic equilibrium (Keldysh, 1964).
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.
In the non-equilibrium Green function calculations, the use of the generalized Kadanoff–Baym ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green function from its time-diagonal value. With this, a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present the results for a two-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for a correct description of the equilibrium and dynamic properties.
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.