This book offers a self-contained introduction to non-equilibrium quantum particle dynamics for inhomogeneous systems, including a survey of recent breakthroughs pioneered by the authors and others. The approach is based on real-time Green’s functions.

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time. In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies and scattering self-energies, are examined and efficient methods for their evaluation are explained. Finally, the application of these methods to study novel electronic devices such as nanotubes, graphene, Si-nanowires and low-dimensional thermoelectric devices and photodetectors are discussed.

Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many areas of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which is equally applied to all these areas is given by quantum field theory. This book provides an overview of the basic ideas and concepts of the method of nonequilibrium Green's functions, written by the leading experts and presented in a way accessible to non-specialists and graduate students. It is complemented by invited review papers on modern applications of the method to a variety of topics, such as optics and quantum transport in semiconductors; superconductivity; strong field effects, QCD, and state-of-the-art computational concepts — from Green's functions to quantum Monte Carlo and time-dependent density functional theory.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transport in dense plasmas and semiconductors; correlations, bound states and coherence; strong field effects and short-pulse lasers; nuclear matter and QCD.Authors include: Gordon Bayan, Pawel Danielewicz, Don DuBois, Hartmut Haug, Klaus Henneberger, Antti-Pekka Jauho, Jörn Kuoll, Dietrich Kremp, Pavel Lipavsky and Paul C Martin.

Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transport in dense plasmas and semiconductors; correlations, bound states and coherence; strong field effects and short-pulse lasers; nuclear matter and QCD.Authors include: Gordon Bayan, Pawel Danielewicz, Don DuBois, Hartmut Haug, Klaus Henneberger, Antti-Pekka Jauho, J”rn Kuoll, Dietrich Kremp, Pavel Lipavsky and Paul C Martin.

This dissertation, "Nonequilibrium Green's Function-hierarchical Equation of Motion Method for Time-dependent Quantum Transport" by Shuguang, Chen, 陈曙光, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The nonequilibrium Green's function-hierarchical equation of motion (NEGFHEOM) method has been developed to simulate the time-dependent electron transport process. The real-time evolution of the reduced single-electron density matrix is solved through the Liouville-von-Neumann equation. The method is very efficient compared to conventional NEGF formulas which need to discretize the simulation time. The hierarchical equation of motion (HEOM) is closed at the second-tier in the time-dependent noninteracting Kohn-Sham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the first-tier. The resulting NEGF-HEOM-WBL method is particularly suitable for simulating the long time transient dynamics for large systems. The method developed is first applied to calculate the transient current through an array of as many as 1000 quantum dots. Upon switching on the bias voltage, the current increases linearly with respect to time before reaching its steady state value. And the time required for the current to reach its steady state value is exactly the time for a conducting electron to travel through the array at Fermi velocity. These phenomena can be understood by simple analysis on the energetics of the quantum dots or by classical electron gas model. Then the method is employed to investigate several simple molecular circuits, in which the para-linkage or meta-linkage benzene acts as the transmitting molecular entity. The simulation results shows that it takes a certain amount of time before the quantum interference manifests itself, and that the transmission through the meta case is hundreds of times smaller than that through the para case. To investigate the quantum interference process in molecular electronics, the concept of Buttiker probe is introduced. The Buttiker probe is an electrode that, when attached to electronic devices, causes the coherence passing through disappear. Simulation results show that the Buttiker probe can enhance the transmission of the meta benzene system through destroying the constructive interference. By turning the probe on and off, it can be observed that large strong correlations are indeed built up as electrons are transported through benzenoid structures - when the decoherence is turned off, the current rises, and when the decoherence is turned back on, the current falls. Finally, TDDFT(B)-NEGF-HEOM-WBL method is implemented to solve realistic systems in the formalism of time-dependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the time-dependent electron transport through a CNT-based device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGF-HEOM-WBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGF-HEOM-WBL method is more suitable. DOI: 10.5353/th_b5312338 Subjects: Quantum theory - Mathematics Green's functions Transport theory