Advanced Solid State Physics (II) [English] – 111Academic Year
This course is provided by NYCU Electrophysics .
This course is the advanced solid state theory. The important fundamental techniques in quantum many-body theory are introduced, such as: Green's functions, Perturbation theory, Diagrammatic expansions, Linear response theory. The goal is to set up the theoretical foundations for graduate students to study more advanced topics in modern solid state physics.
Textbooks：
1. Many-body Quantum Theory in Condensed Matter Physics: an introduction, Henrik Bruus and Karsten Flensberg, Oxford University Press, 2004.
2.Green's functions for solid state physicists, S. Doniach and E.H. Sondeheimer, Imperial College Press, 1998.
3.Quantum Theory of Many-Particle Systems, A. Fetter and J. Walecka, McGraw-Hill, Inc. 1971.
4.Quantum Many-particle systems, J. W. Negele and H. Orland, Addison-Wesley Publishing Company, 1988.
5. Interacting Electrons and Quantum Magnetism, Assa Auerbach, Springer-Verlag, 1994.
For perfect learning results, please buy textbooks!
| Instructor(s) | Department of Electrophysics Prof. Chung-Hou Chung |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 111 Academic Year |
| Level | Graduate Student |
| Prior Knowledge | Advanced Solid State Physics (I) |
| Related Resources | Course Video Course Syllabus |
| Week | Course Content | Course Video |
|---|---|---|
| 1 | Course Outline Introduction and Introduction to Green's Function Methods I | Watch Online |
| 2 | Introduction to Green's Function Methods II | Watch Online |
| 3 | Free Particle Green's Functions I: Linear Response Theory | Watch Online |
| 4 | Application of Green's Functions II | Watch Online |
| 5 | Finite Temperature Green's Function I: Matsubara Formalism | Watch Online |
| 6 | Finite Temperature Green's Function II | Watch Online |
| 7 | Finite Temperature Green's Function III | Watch Online |
| 8 | Finite Temperature Green's Function IV | Watch Online |
| 9 | Perturbation theory: Wick’s Theorem I | Watch Online |
| 10 | Perturbation theory: Wick’s Theorem II | Watch Online |
| 11 | Perturbation theory: Feynman Diagram and Feynman Rules I | Watch Online |
| 12 | Perturbation theory: Feynman Diagram and Feynman Rules II | Watch Online |
| 13 | Perturbation theory: Feynman Diagram and Feynman Rules III | Watch Online |
| 14 | Dyson’s Equation | Watch Online |
| 15 | Application: Disorder and Anderson Localization I | Watch Online |
| 16 | Application: Disorder and Anderson Localization II: Self-Energy correction | Watch Online |
| 17 | Application: Disorder and Anderson Localization III: Kubo Formula | Watch Online |
| 18 | Applicationb: Disorder and Anderson Localization IV: Vertex Correction I | Watch Online |
| 19 | Application: Disorder and Anderson Localization V: Vertex Correction II | Watch Online |
| 20 | Application: Disorder and Anderson localization VI: Vertex Correction III and Random Phase Approximation (RPA) Method | Watch Online |
| 21 | Application: Thomas-Fermi Approximation I: Density-Density Correlation Function | Watch Online |
| 22 | Application: Thomas-Fermi Approximation II | Watch Online |
| 23 | Application: Electron-Phonon Coupling I | Watch Online |
| 24 | Application: Electron-Phonon Coupling II | Watch Online |
| 25 | Application: Electron-Phonon Coupling III | Watch Online |
| 26 | Application: BCS Theory and Cooper Instability I | Watch Online |
| 27 | Applic ation: BCS Theory and Cooper Instability II | Watch Online |
| 28 | Application: Green's Function in BCS Theory | Watch Online |
| 29 | Application: Nambu Formulation of BCS Theory | Watch Online |
Course Objectives
This course is the advanced solid state theory. The important fundamental techniques in quantum many-body theory are introduced, such as: Green's functions, Perturbation theory, Diagramatic expansions, Linear response theory. The goal is to set up the theoretical foundations for graduate students to study more advanced topics in modern solid state physics.
Course Chapter
| Subject | Conetent |
| * Introduction to Green's function | General introduction to Green's function and its applications to solid state experiments. |
| * Free particle Green's functions | Introduce free particle Green's function |
| Finite temperature Green's functions | Introduce finite temperature Green's functions |
| Linear response theory, Masubara formulation | Introduce linear response theory and Masubara formulism together with Green's functions in calculating transport properties of solids |
| perturbation theory | Introduce Perturbation theory, Feynman diagrams and Wick's theorem |
| *Self-energy | Introduce how to calculate self-energy corrections in many-body systems |
| Vertex corrections | Learn the vertex correction part |
| Dyson's equations | This is the approach which can solve self energy and vertex corrections at the same time. |
| Disorder and localization | Apply the above Green's function techniques to a specific quantum many-body system--Anderson localization in solids with impurities/disorder |
| Strongly correlated electron systems | Apply Green's function techniques to the 2nd quantum many-body system-- strongly correlated electron systems. Introduce Hubbard, Heisenberg, and t-J models. Explain magnetic quantum phases and high-Tc superconductivity in cuprates. |
| Kondo effect in quantum impurity systems | Apply Green's function techniques to another strongly correlated system--Kondo system. Explain magnetic properties in metals with impurities. Discuss Kondo effect in quantum dots |
| Introduction to Renormalization Group technique in many-body system | Give a general introduction to renormalization group theory in quantum many-body systems via Green's function approach. |
Reference Books
1. Many-body Quantum Theory in Condensed Matter Physics: an introduction, Henrik Bruus and Karsten Flensberg, Oxford University Press, 2004.
2.Green's functions for solid state physicists, S. Doniach and E.H. Sondeheimer, Imperial College Press, 1998.
3.Quantum Theory of Many-Particle Systems, A. Fetter and J. Walecka, McGraw-Hill, Inc. 1971
4. Quantum Many-particle systems, J. W. Negele and H. Orland, Addison-Wesley Publishing Company, 1988.
5. Interacting Electrons and Quantum Magnetism, Assa Auerbach, Springer-Verlag, 1994.
Scoring criteria
| project | % |
| homework | 70% |
| take-home final exam | 30% |
