多体系统的量子理论

Preface
List of Tables
Basic Concepts
1.1 Introduction： Whys and Hows of Quantum Many-Body Theory
1.1.1 Screening of Coulomb Potential in Metal
1.1.2 Time-Dependent Effects. Plasmons
1.2 Propagation Function in a One-Body Quantum Theory
1.2.1 Propagator： Definition and Properties
1.2.2 Feynmans Formulation of Quantum Mechanics： Path (Functional) Integrals
1.2.3 Quantum Transport in Mesoscopic Rings： Path Integral Description
1.3 Perturbation Theory for the Propagator
1.3.1 General Formalism
1.3.2 An Example： Potential Scattering
1.4 Second Quantization
1.4.1Description of Large Collections of Identical Particles. Focks Space
1.4.2 Bosons
1.4.3 Number and Phase Operators and Their Uncertainty Relation
1.4.4 Fermions
1.5 Problems to Chapter 1
Greens Functions at Zero Temperature
2.1 Greens Function of The Many-Body System： Definition and Properties
2.1.1 Definition of Greens Functions of the Many-Body System
2.I.2 Analytic Properties of Greens Functions
2.1.3 Retarded and Advanced Greens Functions
2.1.4 Greens Function and Observables
2.2 Perturbation Theory： Feynman Diagrams
2.2.1Derivation of Feynman Rules. Wicks and Cancellation Theorems
2.2.2 Operations with Diagrams. Self Energy. Dysons Equation
2.2.3 Renormalization of the Interaction. Polarization Operator
2.2.4 Many-Particle Greens Functions.Bethe-Salpeter Equations. Vertex Function
2.3 Problems to Chapter 2
3 More Greens Functions， Equilibrium and Otherwise，and Their Applications
3. I Analytic Properties of Equilibrium Greens Functions
3.1.1 Statistical Operator (Density Matrix). The Liouville Equation
3.1.2 Definition and Analytic Properties of Equilibrium Greens Functions
3.2 Matsubara formalism
3.2.1 Blochs Equation
3.2.2 Temperature (Matsubara) Greens Function
3.2.3 Perturbation Series and Diagram Techniques for the Temperature Greens Function
3.3 Linear Response Theory
3.3.1 Linear Response Theory. Kubo Formulas
3.3.2 Fluctuation-Dissipation Theorem
3.4 Nonequilibrium Greens Functions
3.4.1Nonequilibrium causal Greens function： definition
3.4.2 Contour Ordering and Three More Nonequilibrium Greens Functions
3.4.3 The Keldysh Formalism
3.5 Quantum Kinetic Equation
3.5.1Dysons Equations for Nonequilibrium Greens Functions
3.5.2 The Quantum Kinetic Equation
3.6 Application： Electrical Conductivity of Quantum Point Contacts
3，6.1 Quantum Electrical Conductivity in the Elastic Limit
3.6.2 Elastic Resistance of a Point Contact： Sharvin Resistance， the Landauer Formula， and Conductance Quantization
3.6.3 The Electron-Phonon Collision Integral in 3 D Quantum Point Contact
3.6.4 "Calculation of the Inelastic Component of the Point Contact Current
3.7 Method of Tunneling Hamiltonian
3.8 Problems to Chapter 3
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
4.3.1 Derivation of the BCS Hamiltonian
4.3.2 Diagonalization of the BCS Hamiltonian. The Bogoliubov transformation. Bogoliubov-de Gennes Equations
4.3.3 Bogolons
4.3.4 Thermodynamic Potential of a Superconductor
4.4 Greens Functions of a Superconductor：The Nambu-Gorkov Formalism
4.4.1Matrix Structure of the Theory
4.4.2 Elements of the Strong Coupling Theory
4.4.3 Gorkovs Equations for the Greens Functions
4.4.4 Current-Carrying State of the Superconductor
4.4.5 Destruction of Superconductivity by Current
4.5 Andreev Reflection
4.5.1 The Proximity Effect in a Normal Metal in Contact With a Superconductor
4.5.2 Andreev Levels and Josephson Effect in a Clean SNS Junction
4.5.3 Josephson Current in a Short Ballistic Junction.Quantization of Critical Current
in Quantum Point Contact
4.5.4 Josephson Current in a Long SNS Junction
4.5.5 "Transport in Superconducting Quantum Point Contact： The Keldysh Formalism Approach
4.6 Tunneling of Single Electrons and Cooper Pairs
4.6.1Coulomb Blockade of Single-Electron Tunneling
4.6.2 Superconducting Grain： When One Electron Is Too Many.
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 Andrecv
Interferometers
References
Index