The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics.

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in\ud order to deal with the time-dependent current response of a resonant tunneling system. We use a partition-free\ud approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No\ud fictitious partitions are used. Despite a more involved formulation, this partition-free approach has many\ud appealing features being much closer to what is experimentally done. In particular, besides the steady-state\ud responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under\ud what circumstances a steady-state current develops and compare our result with the one obtained in the\ud partitioned scheme. We prove a theorem of asymptotic equivalence between the two schemes for arbitrary\ud time-dependent disturbances. We also show that the steady-state current is independent of the history of the\ud external perturbation\ud ~\ud memory-loss theorem\ud !\ud . In the so-called wide-band limit an analytic result for the time-\ud dependent current is obtained. In the interacting case we work out the lesser Green function in terms of the\ud self-energy and we recover a well-known result in the long-time limit. In order to overcome the complications\ud arising from a self-energy which is nonlocal in time we propose an exact nonequilibrium Green-function\ud approach based on time-dependent density-functional theory. The equations are no more difficult than an\ud ordinary mean-field treatment. We show how the scattering-state scheme by Lang follows from our formula-\ud tion. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is\ud obtained. As an example the time-dependent current response is calculated in the random-phase approximation

We present a computationally tractable scheme of time-dependent transport phenomena within open-boundary time-dependent density-functional-theory. Within this approach all the response properties of a system are determined from the time-propagation of the set of "occupied" KohnSham orbitals under the influence of the external bias. This central idea is combined with an openboundary description of the geometry of the system that is divided into three regions: left/right leads and the device region ("real simulation region"). We have derived a general scheme to extract the set of initial states in the device region that will be propagated in time with proper transparent boundary-condition at the device/lead interface. This is possible due to a new modified Crank-Nicholson algorithm that allows an efficient time-propagation of open quantum systems. We illustrate the method in one-dimensional model systems as a first step towards a full first-principles implementation. In particular we show how a stationary current develops in the system independent of the transient-current history upon application of the bias. The present work is ideally suited to study ac transport and photon-induced charge-injection. Although the implementation has been done assuming clamped ions, we discuss how it can be extended to include dissipation due to electron-phonon coupling through the combined simulation of the electron-ion dynamics as well as electron-electron correlations.

We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time-propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch-on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time-dependence of these observables provides a wealth of information on the level structure of the quantum wire out of equilibrium. For moderate interaction strenghts the 2B and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.

We study time-dependent quantum transport in a correlated model system by means of timepropagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green function. We consider an initially contacted equilibrium system of a correlated central region coupled to tight-binding leads. Subsequently a time-dependent bias is switched on after which we follow in detail the time-evolution of the system. Important features of the Kadanoff-Baym approach are 1) the possibility of studying 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 find that initial correlation and memory terms due to many-body interactions have a large effect on the transient currents. Furthermore the value of the steady state current is found to be strongly dependent on the approximation used to treat the electronic interactions.PACS numbers: 72.10. Bg,85.30.Mn The ultimate goal of molecular electronics [1] in solid state circuitry is to miniaturize the size and maximize the speed of integrated devices. Advances in this field crucially depend on the accumulated experimental and theoretical knowledge. For the latter to progress it is essential to develop quantum mechanical approaches that are able to deal with open and interacting systems in an out of steady-state regime. Desirable features of such approaches are therefore 1) the possibility to study the ultrafast dynamics of transients and other time-dependent (TD) regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. Feature 1) was incorporated in some recently proposed oneparticle frameworks and was exploited to address several issues in TD quantum transport (QT) [2,3,4,5]. These frameworks can, in principle, be combined with TD density functional theory [6,7,8,9], thus providing a route to include Coulomb interactions (possibly in a conserving way [10]). Feature 2) is an essential requirement as realistic time evolutions must preserve basic conservation laws as, for instance, the continuity equation. Conserving approximations [11] like, e.g. self-consistent Hartree-Fock (HF), second Born (2B) or GW, have recently been employed in the context of QT but the implementations have been, sofar, restricted to steady-state regimes [12,13,14,15,16]. In this Letter we propose an alternative approach to TD-QT that encompasses both feature 1) and 2). It is based on the real-time propagation of the embedded Kadanoff-Baym (KB) equations [17,18,19,20] which are equations of motion for the nonequilibrium Green function from which basic properties of the system can be calculated. We consider a set {α} of noninteracting electronic reservoirs connected via a tunneling Hamiltonian to an interacting many-body quantum system C. The Green function G(z, z ′ ) (we suppress basis indices) projected on C obeys the equation of motion [18,19] where z and z ′ are time-coordinates on the Keldysh contour c [19]. We consider systems initially (times...