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.

No abstract

No abstract

We show that a time-dependent particle density n͑rt͒ obtained from a given many-particle system can, under mild restrictions on the initial state, always be reproduced by an external potential y 0 ͑rt͒ in a many-particle system with different two-particle interactions. Given the initial state of this other manyparticle system, the potential y 0 ͑rt͒ is unique up to a purely time-dependent function. As a special case we obtain the well-known Runge-Gross theorem. [S0031-9007(99)09067-5] PACS numbers: 71.15.Mb, 31.10. + z, 31.15.Ew In this work we will discuss the relation between the density and potential of time-dependent many-particle systems. We will show that a time-dependent particle density n͑rt͒ obtained from a given many-particle system can, under mild restrictions on the initial state, always be reproduced by an external potential y 0 ͑rt͒ in a many-particle system with different two-particle interactions. Given the initial state of this other many-particle system the potential y 0 ͑rt͒ is unique up to a purely time-dependent function.If we specialize to two systems with identical initial states and identical two-particle interactions this statement reduces to the well-known Runge-Gross theorem [1]. This work therefore represents an extension of the theorem by Runge and Gross. Another special case is obtained if we take the two-particle interactions of the second system to be zero. In that case we obtain the result that the density of an interacting system can be reproduced by a one-body potential in a noninteracting system. This result has important consequences for timedependent density functional theory (TDDFT).TDDFT [2][3][4][5] has turned out to be a successful approach to the calculation of time-dependent properties of many-particle systems. The rigorous foundation of the TDDFT approach is based on the Runge-Gross theorem [1]. This theorem states that, for a fixed initial manybody state, there is a one-to-one correspondence between the time-dependent external field y͑rt͒ and the timedependent density n͑rt͒. This is made into a practical scheme by means of the so-called Kohn-Sham equations. In the Kohn-Sham approach one introduces a noninteracting many-particle system with the same density n͑rt͒ as the fully interacting system. This noninteracting KohnSham system has a local potential that incorporates all the exchange-correlation effects and is obtained as a density derivative of the action [6]. The fact that the Kohn-Sham equations constitute a set of one-particle equations makes them of great practical use. However, it has still been an unproven assumption that such a noninteracting system, with the same density as the fully interacting system at all times, exists. If, for a certain density n͑rt͒, such a noninteracting system exists then this density is called noninteracting y-representable.There are, however, some differences between the use of this concept in stationary and time-dependent systems. For stationary systems a density n͑r͒ is called noninteracting y representable if this density ca...

No abstract

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 give an overview of the underlying concepts of time-dependent density-functional theory. The basic relations between densities, potentials and initial states, for time-dependent many-body systems are discussed. We obtain some new results concerning the invertability of response functions. Some fundamental difficulties associated with the time-dependent action principle are discussed and we show how these difficulties can be resolved by means of the Keldysh formalism.

We solve the long-standing problem of the large overestimation of the static polarizability of conjugated polymers obtained using the local density approximation within density-functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation (xc) effects found in these quasi-one-dimensional systems. Time-dependent current-density-functional theory enables a local current description of ultranonlocal xc effects using the Vignale-Kohn functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)]. Except for the model hydrogen chain, our results are in excellent agreement with the best available correlated methods.