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• W1566014229 abstract "1 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 Feynman's 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.- 1.4.1 Description of Large Collections of Identical Particles. Fock's 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.- 2 Green's Functions at Zero Temperature.- 2.1 Green's Function of The Many-Body System: Definition and Properties.- 2.1.1 Definition of Green's Functions of the Many-Body System.- 2.1.2 Analytic Properties of Green's Functions.- 2.1.3 Retarded and Advanced Green's Functions.- 2.1.4 Green's Function and Observables.- 2.2 Perturbation Theory: Feynman Diagrams.- 2.2.1 Derivation of Feynman Rules. Wick's and Cancellation Theorems.- 2.2.2 Operations with Diagrams. Self Energy. Dyson's Equation.- 2.2.3 Renormalization of the Interaction. Polarization Operator.- 2.2.4 Many-Particle Green's Functions. Bethe-Salpeter Equations. Vertex Function.- 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.- 3.1.1 Statistical Operator (Density Matrix). The Liouville Equation.- 3.1.2 Definition and Analytic Properties of Equilibrium Green's Functions.- 3.2 Matsubara formalism.- 3.2.1 Bloch's Equation.- 3.2.2 Temperature (Matsubara) Green's Function.- 3.2.3 Perturbation Series and Diagram Techniques for the Temperature Green's Function.- 3.3 Linear Response Theory.- 3.3.1 Linear Response Theory. Kubo Formulas.- 3.3.2 Fluctuation-Dissipation Theorem.- 3.4 Nonequilibrium Green's Functions.- 3.4.1 Nonequilibrium causal Green's function: definition.- 3.4.2 Contour Ordering and Three More Nonequilibrium Green's Functions.- 3.4.3 The Keldysh Formalism.- 3.5 Quantum Kinetic Equation.- 3.5.1 Dyson's Equations for Nonequilibrium Green's 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 133.- 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.- 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.- 4.3.1 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 Green's Functions of a Superconductor: The Nambu-Gor'kov Formalism.- 4.4.1 Matrix Structure of the Theory.- 4.4.2 Elements of the Strong Coupling Theory.- 4.4.3 Gorkov's Equations for the Green's 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.- 4.6.1 Coulomb 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 Andreev Interferometers.- References." @default.
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• W1566014229 date "2012-10-17" @default.
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• W1566014229 title "Quantum Theory of Many-Body Systems: Techniques and Applications" @default.
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