The Quantum Mechanics Of Many Body Systems
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Quantum Theory of Many-Body Systems
Author: Alexandre Zagoskin
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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
The Quantum Mechanics of Many-Body Systems
"Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.
Physics and Mathematics of Quantum Many-Body Systems
This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.