UID:
almahu_9949199332202882
Format:
XV, 229 p.
,
online resource.
Edition:
1st ed. 1998.
ISBN:
9781461205951
Series Statement:
Graduate Texts in Contemporary Physics,
Content:
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.
Note:
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 Nambu-Gor'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 Landauer-Lambert formula -- A.2 Giant Conductance Oscillations in Ballistic Andreev Interferometers -- References.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9780387983844
Additional Edition:
Printed edition: ISBN 9781461268314
Additional Edition:
Printed edition: ISBN 9781461205968
Language:
English
DOI:
10.1007/978-1-4612-0595-1
URL:
https://doi.org/10.1007/978-1-4612-0595-1
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