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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.

This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green's functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals.This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems.Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume and which therefore provides an ideal testing ground for many-body theories.

In this edition the second and main part of the book has been considerably expanded as to cover important applications of the formalism. In Chap.5 a section was added outlining the extensive role of the tight­ binding (or equivalently the linear combination of atomic-like orbitals) approach to many branches of solid-state physics. Some additional informa­ tion (including a table of numerical values) regarding square and cubic lattice Green's functions were incorporated. In Chap.6 the difficult subjects of superconductivity and the Kondo effect are examined by employing an appealingly simple connection to the question of the existence of a bound state in a very shallow potential well. The existence of such a bound state depends entirely on the form of the un­ perturbed density of states near the end of the spectrum: if the density of states blows up there is always at least one bound state. If the density of states approaches zero continuously, a critical depth (and/or width) of the well must be reached in order to have a bound state. The borderline case of a finite discontinuity (which is very important to superconductivity and the Kondo effect) always produces a bound state with an exponentially small binding energy.

Quarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound states. This phenomenon is called confinement and has been a central research topic of elementary particle physics for the last few decades. In order to find the mechanism that forbids the existence of free quarks many approaches and ideas are being followed, but by now it has become clear that they are not mutually exclusive but illuminate the problem from different perspectives. Two such confinement scenarios are investigated in this thesis: Firstly, the importance of Abelian field components for the low-energy regime is corroborated, thus supporting the dual superconductor picture of confinement and secondly, the influence of the Gribov horizon on non-perturbative solutions is studied.

Nanoscale miniaturization and femtosecond laser-pulse spectroscopy require a quantum mechanical description of the carrier kinetics that goes beyond the conventional Boltzmann theory. On these extremely short length and time scales, the electrons behave as do partially coherent waves. This monograph deals with quantum kinetics for transport in low-dimensional microstructures and for ultra-short laser pulse spectroscopy. The nonequilibrium Green function theory is described and used for the derivation of the quantum kinetic equations. Numerical methods for the solution of the retarded quantum kinetic equations are discussed and results are presented for high-field transport and for mesoscopic transport phenomena. Quantum beats, polarization decay, and non-Markovian behaviour are treated for femtosecond spectroscopy on a microscopic basis. Since the publishing of the first edition in 1996, the nonequilibrium Green function technique has been applied to a large number of new research topics, and the revised edition introduces the reader to many of these areas, such as molecular electronics, noise calculations, build-up of screening and polaron correlations, and non-Markovian relaxation, among others. Connection to recent experiments is made, and it is emphasized how the quantum kinetic theory is essential in their interpretation.

The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of'difficult'questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

Intended for graduate students in physics and related fields, this text is a self contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green's functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero- temperature perturbation theory, and the Matsubara, Keldysh, and Nambu -Gor'kov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable the student to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume, and which therefore provides an ideal testing ground for many-body theories. The book begins by introducing the Green's function for one-particle systems (using Feynman path integrals), general perturbation theory, and second quantization. It then turns to the usual zero-temperature formalism, discussing the properties and physical meaning of the Green's function for many-body systems and then developing the diagram techniques of perturbation theory. The theory is extended to finite temperatures, including a discussion of the Matsubara formalism as well as the Keldysh technique for essentially nonequilibrium systems. The final chapter is devoted to applications of the techniques to superconductivity, incuding discussions of the superconducting phase transition, elementary excitations, transport, Andreev reflections, and Josephson junctions. Problems at the end of each chapter help to guide learning an to