Spectroscopic probes of quantum matter
Spectrum analysis Quantum theory
IOP Publishing
2018
EISBN 9780750317412
1. Introduction.
1.1. Nuclear scattering and density-density correlation function.
1.2. Linear response and retarded correlation functions.
1.3. Thermodynamic properties and Green's function
part I. Digest of many-body theory. 2. Elements of quantum mechanics.
2.1. Thermodynamics of quantum systems.
2.2. Time dependence.
2.3. Second quantization.
2.4. Independent electrons.
2.5. Phonons.
2.6. Magnons
3. Correlation functions : definitions and properties.
3.1. A zoo of correlation functions.
3.2. Lehmann spectral representation.
3.3. Independent particles.
3.4. Analytic properties and sum rules
4. Imaginary-time formalism.
4.1. Motivation.
4.2. Correlation functions in imaginary time.
4.3. Analytic continuation
5. Calculating correlation functions.
5.1. Perturbation theory and Feynman diagrams.
5.2. Equation-of-motion method
6. Response of matter to applied fields.
6.1. Linear and quadratic response.
6.2. Response functions, susceptibilities.
6.3. Examples of couplings.
6.4. Response functions and imaginary-time functions
part II. Spectroscopic probes. 7. External photoemission (XPS, PES, ARPES).
7.1. Response theory of external photoemission.
7.2. Sudden approximation and spectral function.
7.3. The notion of quasi-particle.
7.4. Beyond the sudden approximation
8. Electrical resistivity.
8.1. Kubo formula for conductivity.
8.2. Derivation of the Drude formula.
8.3. Residual resistivity of metals and impurity scattering.
8.4. T2 law and electron-electron interaction.
8.5. Magnetic impurities and Kondo effect.
8.6. Effects beyond quasi-particle scattering
9. Electron tunneling.
9.1. Electron tunneling : a phenomenon out of equilibrium.
9.2. Tunneling-Hamiltonian formalism.
9.3. The tunneling matrix element.
9.4. DOS and electron dispersion.
9.5. LDOS as seen by STM
10. Neutron scattering.
10.1. The differential scattering cross section.
10.2. Nuclear scattering.
10.3. Magnetic scattering.
The contemporary understanding of matter is based on the quantum theory, which envisions large collections of particles interacting with each other and with their environment. Spectroscopic probes based for instance on light change the environment and trigger a collective response of the particles. This book based on a graduate-level course explains the underpinnings of many-body quantum theory and exposes the main methodologies for calculations, before describing, with the support of practical examples and short computer codes, how the spectroscopic techniques are represented within the theory and how their outcome is interpreted as a probe of the correlations between quantum particles.
1.1. Nuclear scattering and density-density correlation function.
1.2. Linear response and retarded correlation functions.
1.3. Thermodynamic properties and Green's function
part I. Digest of many-body theory. 2. Elements of quantum mechanics.
2.1. Thermodynamics of quantum systems.
2.2. Time dependence.
2.3. Second quantization.
2.4. Independent electrons.
2.5. Phonons.
2.6. Magnons
3. Correlation functions : definitions and properties.
3.1. A zoo of correlation functions.
3.2. Lehmann spectral representation.
3.3. Independent particles.
3.4. Analytic properties and sum rules
4. Imaginary-time formalism.
4.1. Motivation.
4.2. Correlation functions in imaginary time.
4.3. Analytic continuation
5. Calculating correlation functions.
5.1. Perturbation theory and Feynman diagrams.
5.2. Equation-of-motion method
6. Response of matter to applied fields.
6.1. Linear and quadratic response.
6.2. Response functions, susceptibilities.
6.3. Examples of couplings.
6.4. Response functions and imaginary-time functions
part II. Spectroscopic probes. 7. External photoemission (XPS, PES, ARPES).
7.1. Response theory of external photoemission.
7.2. Sudden approximation and spectral function.
7.3. The notion of quasi-particle.
7.4. Beyond the sudden approximation
8. Electrical resistivity.
8.1. Kubo formula for conductivity.
8.2. Derivation of the Drude formula.
8.3. Residual resistivity of metals and impurity scattering.
8.4. T2 law and electron-electron interaction.
8.5. Magnetic impurities and Kondo effect.
8.6. Effects beyond quasi-particle scattering
9. Electron tunneling.
9.1. Electron tunneling : a phenomenon out of equilibrium.
9.2. Tunneling-Hamiltonian formalism.
9.3. The tunneling matrix element.
9.4. DOS and electron dispersion.
9.5. LDOS as seen by STM
10. Neutron scattering.
10.1. The differential scattering cross section.
10.2. Nuclear scattering.
10.3. Magnetic scattering.
The contemporary understanding of matter is based on the quantum theory, which envisions large collections of particles interacting with each other and with their environment. Spectroscopic probes based for instance on light change the environment and trigger a collective response of the particles. This book based on a graduate-level course explains the underpinnings of many-body quantum theory and exposes the main methodologies for calculations, before describing, with the support of practical examples and short computer codes, how the spectroscopic techniques are represented within the theory and how their outcome is interpreted as a probe of the correlations between quantum particles.
