Quantum Theory of Many-Body Systems

Based on a course given at Chalmers Technical University in Goteborg, Sweden, this text is intended for graduate students in physics and related fields. It provides a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The aim is not to be exhaustive, but to present just enough detail to enable the student to follow the current research literature. Many of the examples are drawn from mesoscopic physics, a rapidly developing field that deals with systems small enough that quantum coherence is maintained throughout their volume, providing an ideal testing ground for many-body theories. Problems at the end of each chapter help to guide learning an to illustrate the applications of the formalism.

Uses the traditional mathematical formalism of quasiparticles and Green`s functions. Covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory, and the Matsubara, Keldysh, and Nambu-Gorov formalisms. Presents enough detail to enable the reader to follow the current research literature or to apply the techniques to new problems. Includes many of the examples drawn from mesoscopic physics, which provides an ideal testing ground for many-body theories. Includes applications of the techniques. Problems at the end of each chapter help to guide learning and illustrate the applications.

Inhalt
1 Basic Concepts.- 1.1 Introduction: Whys and Hows of Quantum Many-Body Theory.- 1.2 Propagation Function in a One-Body Quantum Theory.- 1.3 Perturbation Theory for the Propagator.- 1.4 Second Quantization.- 1.5 Problems to Chapter 1.- 2 Green's Functions at Zero Temperature.- 2.1 Green's Function of The Many-Body System: Definition and Properties.- 2.2 Perturbation Theory: Feynman Diagrams.- 2.3 Problems to Chapter 2.- 3 More Green's Functions, Equilibrium and Otherwise, and Their Applications.- 3.1 Analytic Properties of Equilibrium Green's Functions.- 3.2 Matsubara formalism.- 3.3 Linear Response Theory.- 3.4 Nonequilibrium Green's Functions.- 3.5 Quantum Kinetic Equation.- 3.6 Application: Electrical Conductivity of Quantum Point Contacts.- 3.7 Method of Tunneling Hamiltonian.- 3.8 Problems to Chapter 3.- 4 Methods of the Many-Body Theory in Superconductivity.- 4.1 Introduction: General Picture of the Superconducting State.- 4.2 Instability of the Normal State.- 4.3 Pairing (BCS) Hamiltonian.- 4.4 Green's Functions of a Superconductor: The NambuGor'kov Formalism.- 4.5 Andreev Reflection.- 4.6 Tunneling of Single Electrons and Cooper Pairs.- 4.7 Problems to Chapter 4.- A Landauer Formalism for Hybrid Normal-Superconducting.- Structures.- A.1 The LandauerLambert formula.- A.2 Giant Conductance Oscillations in Ballistic Andreev Interferometers.- References.