高等固態物理(二) [English] – 111學年度
本課程是由 國立陽明交通大學電子物理系提供。
這門課程主要介紹量子多體理論中的重要基礎技術，包括：格林函數(Green's functions)、微擾理論 (Perturbation theory)、(Diagrammatic expansions)和線性響應理論(Linear response theory)。課程目標是為研究生奠定理論基礎，以便他們進一步研究現代固態物理中的高階主題。
課程用書：
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.
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| 授課教師 | 電子物理系 仲崇厚老師 |
|---|---|
| 課程學分 | 3學分 |
| 授課年度 | 111學年度 |
| 授課對象 | 研究所 |
| 預備知識 | Advanced Solid State Physics (I) |
| 課程提供 | 課程影音 課程綱要 |
| 週次 | 課程內容 | 課程影音 |
|---|---|---|
| 1 | 課程大綱介紹與格林函數簡介(一) | 線上觀看 |
| 2 | 格林函數簡介(二) | 線上觀看 |
| 3 | 自由粒子格林函數(一)：線性響應理論 | 線上觀看 |
| 4 | 自由粒子格林函數(二)：格林函數之應用 | 線上觀看 |
| 5 | 有限溫度格林函數(一)：Matsubara 頻率之表示形式 | 線上觀看 |
| 6 | 有限溫度格林函數(二) | 線上觀看 |
| 7 | 有限溫度格林函數(三) | 線上觀看 |
| 8 | 有限溫度格林函數(四) | 線上觀看 |
| 9 | 微擾理論：Wick定理(一) | 線上觀看 |
| 10 | 微擾理論：Wick定理(二) | 線上觀看 |
| 11 | 微擾理論：費曼圖與費曼規則(一) | 線上觀看 |
| 12 | 微擾理論：費曼圖與費曼規則(二) | 線上觀看 |
| 13 | 微擾理論：費曼圖與費曼規則(三) | 線上觀看 |
| 14 | Dyson方程 | 線上觀看 |
| 15 | 應用：無序與Anderson局域化理論(一) | 線上觀看 |
| 16 | 應用：無序與Anderson局域化理論(二)：自能量修正 | 線上觀看 |
| 17 | 應用：無序與Anderson局域化理論(三)：庫波公式 | 線上觀看 |
| 18 | 應用：無序與Anderson局域化理論(四)：頂點校正(一) | 線上觀看 |
| 19 | 應用：無序與Anderson局域化理論(五)：頂點校正(二) | 線上觀看 |
| 20 | 應用：Anderson局域化理論(六)：頂點校正(三)與隨機相位近似方法 | 線上觀看 |
| 21 | 應用：托馬斯費米近似(一)：密度-密度關聯函數 | 線上觀看 |
| 22 | 應用：托馬斯費米近似(二) | 線上觀看 |
| 23 | 應用：電子聲子耦合(一) | 線上觀看 |
| 24 | 應用：電子聲子耦合(二) | 線上觀看 |
| 25 | 應用：電子聲子耦合(三) | 線上觀看 |
| 26 | 應用：BCS理論 - 庫柏不穩定性(一) | 線上觀看 |
| 27 | 應用：BCS理論 - 庫柏不穩定性(二) | 線上觀看 |
| 28 | 應用：BCS理論中的格林函數 | 線上觀看 |
| 29 | 應用：BCS理論中的Nambu表述 | 線上觀看 |
課程概述與目標
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.
課程章節
| 單元主題 | 內容綱要 |
| * 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. |
課程書目
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.
評分標準
| 項目 | 百分比 |
| homework | 70% |
| take-home final exam | 30% |