Abstract In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
Abstract In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
This book presents an up-to-date formalism of non-equilibrium Green's functions covering different applications ranging from solid state physics, plasma physics, cold atoms in optical lattices up to relativistic transport and heavy ion collisions. Within the Green's function formalism, the basic sets of equations for these diverse systems are similar, and approximations developed in one field can be adapted to another field. The central object is the self-energy which includes all non-trivial aspects of the system dynamics. The focus is therefore on microscopic processes starting from elementary principles for classical gases and the complementary picture of a single quantum particle in a random potential. This provides an intuitive picture of the interaction of a particle with the medium formed by other particles, on which the Green's function is built on.
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.
The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly
The framework of nonequilibrium Green functions (NEGFs) is developed to accurately describe interacting quantum systems evolving in the presence of strongly exciting ultra-fast fields.At its core stands the selfconsistent determination of the selfenergy, a functional of the single-particle Green function, which incorporates all relevant many-body physics and, via diagrammatic techniques, guarantees the conservation of the constants of motion.Over the last decades, NEGFs have been successfully applied to a broad range of domains ranging from homogeneous systems such as non-ideal quantum gases and plasmas over condensed matter to highly inhomogeneous systems such as atoms and molecules photo-ionized by laser-fields or colliding nuclear matter.Only recently, the first accurate simulation of the expansion dynamics of clouds of ultra-cold fermionic atoms in a two-dimensional optical lattice could be achieved using NEGFs.The single-particle Green function is the solution of a coupled set of kinetic equations.Its intrinsic dependence on two independent time-arguments, ranging over the complete past of the system, not only enables the determination of all singleparticle observables but also provides access to important two-particle observables and spectral information.With this coupling to the history, though, comes the practical necessity to apply physically motivated approximation techniques to the structure of the selfenergy and the Green functions, to achieve numerical tractability.This thesis is devoted to provide a thorough overview of the possible approximation techniques including perturbative and non-perturbative approaches.Starting from the exact coupled set of equations of motion for the Green functions, the expressions for all selfenergy approximations are derived in the most general basis representation, i.e., for interaction tensor elements w ijkl .From this, the corresponding expressions in a diagonal basis, where the interaction can be described as a matrix w ij , and for the special case of the Hubbard model, where the interaction is just given as a scalar U , are deduced.
The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.
The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.