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Feynman diagram techniques in condensed matter physics /
"A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and offers a review of the essential elements of quantum mechanics, solid state physics and statistical mechanics. Alongside a detailed account of the...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface
- 1 A brief review of quantum mechanics
- 1.1 The postulates
- (I) The quantum state
- (II) Observables
- (III) Time evolution
- (IV) Measurements
- (V) Wave function of a system of identical particles
- 1.2 The harmonic oscillator
- Further reading
- Problems
- 2 Single-particle states
- 2.1 Introduction
- 2.2 Electron gas
- 2.3 Bloch states
- 2.4 Example: one-dimensional lattice
- 2.5 Wannier states
- 2.6 Two-dimensional electron gas in a magnetic field
- Further reading
- Problems
- 3 Second quantization
- 3.1 N-particle wave function
- 3.2 Properly symmetrized products as a basis set
- 3.3 Three examples
- 3.4 Creation and annihilation operators
- 3.5 One-body operators
- 3.6 Examples
- 3.7 Two-body operators
- 3.8 Translationally invariant system
- 3.9 Example: Coulomb interaction
- 3.10 Electrons in a periodic potential
- 3.11 Field operators
- Further reading
- Problems
- 4 The electron gas
- 4.1 The Hamiltonian in the jellium model
- 4.2 High density limit
- 4.3 Ground state energy
- Further reading
- Problems
- 5 A brief review of statistical mechanics
- 5.1 The fundamental postulate of statistical mechanics
- 5.2 Contact between statistics and thermodynamics
- 5.3 Ensembles
- 5.4 The statistical operator for a general ensemble
- 5.5 Quantum distribution functions
- Further reading
- Problems
- 6 Real-time Green's and correlation functions
- 6.1 A plethora of functions
- 6.2 Physical meaning of Green's functions
- 6.3 Spin-independent Hamiltonian, translational invariance
- 6.4 Spectral representation
- 6.5 Example: Green's function of a noninteracting system
- 6.6 Linear response theory
- 6.7 Noninteracting electron gas in an external potential
- 6.8 Dielectric function of a noninteracting electron gas.
- 6.9 Paramagnetic susceptibility of a noninteracting electron gas
- 6.10 Equation of motion
- 6.11 Example: noninteracting electron gas
- 6.12 Example: an atom adsorbed on graphene
- Further reading
- Problems
- 7 Applications of real-time Green's functions
- 7.1 Single-level quantum dot
- 7.2 Quantum dot in contact with a metal: Anderson's model
- 7.3 Tunneling in solids
- Further reading
- Problems
- 8 Imaginary-time Green's and correlation functions
- 8.1 Imaginary-time correlation function
- 8.2 Imaginary-time Green's function
- 8.3 Significance of the imaginary-time Green's function
- 8.4 Spectral representation, relation to real-time functions
- 8.5 Example: Green's function for noninteracting particles
- 8.6 Example: Green's function for 2-DEG in a magnetic field
- 8.7 Green's function and the U-operator
- 8.8 Wick's theorem
- 8.9 Case study: first-order interaction
- 8.10 Cancellation of disconnected diagrams
- Further reading
- Problems
- 9 Diagrammatic techniques
- 9.1 Case study: second-order perturbation in a system of fermions
- 9.2 Feynman rules in momentum-frequency space
- 9.3 An example of how to apply Feynman rules
- 9.4 Feynman rules in coordinate space
- 9.5 Self energy and Dyson's equation
- 9.6 Energy shift and the lifetime of excitations
- 9.7 Time-ordered diagrams: a case study
- 9.8 Time-ordered diagrams: Dzyaloshinski's rules
- Further reading
- Problems
- 10 Electron gas: a diagrammatic approach
- 10.1 Model Hamiltonian
- 10.2 The need to go beyond first-order perturbation theory
- 10.3 Second-order perturbation theory: still inadequate
- 10.4 Classification of diagrams according to the degree of divergence
- 10.5 Self energy in the random phase approximation (RPA)
- 10.6 Summation of the ring diagrams
- 10.7 Screened Coulomb interaction.
- 10.8 Collective electronic density fluctuations
- 10.9 How do electrons interact?
- 10.10 Dielectric function
- 10.11 Plasmons and Landau damping
- 10.12 Case study: dielectric function of graphene
- Further reading
- Problems
- 11 Phonons, photons, and electrons
- 11.1 Lattice vibrations in one dimension
- 11.2 One-dimensional diatomic lattice
- 11.3 Phonons in three-dimensional crystals
- 11.4 Phonon statistics
- 11.5 Electron-phonon interaction: rigid-ion approximation
- 11.6 Electron-LO phonon interaction in polar crystals
- 11.7 Phonon Green's function
- 11.8 Free-phonon Green's function
- 11.9 Feynman rules for the electron-phonon interaction
- 11.10 Electron self energy
- 11.11 The electromagnetic field
- 11.12 Electron-photon interaction
- 11.13 Light scattering by crystals
- 11.14 Raman scattering in insulators
- Further reading
- Problems
- 12 Superconductivity
- 12.1 Properties of superconductors
- 12.2 The London equation
- 12.3 Effective electron-electron interaction
- 12.4 Cooper pairs
- 12.5 BCS theory of superconductivity
- 12.6 Mean field approach
- 12.7 Green's function approach to superconductivity
- 12.8 Determination of the transition temperature
- 12.9 The Nambu formalism
- 12.10 Response to a weak magnetic field
- 12.11 Infinite conductivity
- Further reading
- Problems
- 13 Nonequilibrium Green's function
- 13.1 Introduction
- 13.2 Schrodinger, Heisenberg, and interaction pictures
- 13.3 The malady and the remedy
- 13.4 Contour-ordered Green's function
- 13.5 Kadanoff-Baym and Keldysh contours
- 13.6 Dyson's equation
- 13.7 Langreth rules
- 13.8 Keldysh equations
- 13.9 Steady-state transport
- 13.10 Noninteracting quantum dot
- 13.11 Coulomb blockade in the Anderson model
- Further reading
- Problems
- Appendix A: Second quantized form of operators
- A.1 Fermions.
- A.2 Bosons
- Appendix B: Completing the proof of Dzyaloshinski's rules
- Appendix C: Lattice vibrations in three dimensions
- C.1 Harmonic approximation
- C.2 Classical theory of lattice vibrations
- C.3 Vibrational energy
- C.4 Quantum theory of lattice vibrations
- Appendix D: Electron-phonon interaction in polar crystals
- D.1 Polarization
- D.2 Electron-LO phonon interaction
- References
- Index.