多體物理
Many Body Physics
| 節 | 週一 |
|---|---|
5 13:20–14:10 | 多體物理 SC159 3 節連堂 |
6 14:20–15:10 | |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
The physical world, from the behavior of electrons in solids to the structure of atomic nuclei and the properties of quantum fluids, is fundamentally governed by the interactions between a vast number of constituent particles. While single-particle descriptions provide a crucial starting point, they typically fall short in capturing the rich physics of collective phenomena and emergent properties that arise solely from these interactions. Phenomena such as superconductivity, magnetism, the fractional quantum Hall effect, and the properties of strongly correlated materials cannot be understood without a theoretical framework capable of addressing the complex interplay of many interacting degrees of freedom. Thr course "Many-Body Physics" provides a formal introduction to the theoretical tools and conceptual frameworks necessary for describing interacting systems that underlie much of modern condensed matter physics, quantum chemistry, nuclear physics, and even aspects of high-energy physics. A solid grasp of many-body theory is indispensable for students aspiring to conduct research in these areas, as it equips them with the language and techniques to analyze experimental observations, predict new phenomena, and contribute to the development of novel materials and technologies. This course serves as a crucial bridge between foundational quantum mechanics and statistical mechanics and the advanced topics encountered in contemporary research literature and specialized fields.
Quantum mechanics & statistical physics
Homework and lass participation: 50 % Final Exam: 50 %
| 週次 | 主題 |
|---|---|
| 第 1 週 | Overview: From quantum gases to quantum phases |
| 第 2 週 | Fields and particles, 2nd quantization |
| 第 3 週 | Popular models of condensed matter |
| 第 4 週 | Green function and its comrades I: equation of motion, resolvent, 2 and higher point, etc. |
| 第 5 週 | Green function and its comrades II: Matsubara, analytic continuation |
| 第 6 週 | Diagrammatic perturbation theory I: time-evolution operator & PT |
| 第 7 週 | Diagrammatic perturbation theory II: Wick’s theorem, self-energy |
| 第 8 週 | Diagrammatic perturbation theory III: linked cluster, Hartree-Fock, |
| 第 9 週 | Diagrammatic perturbation theory IV: classes of diagrams, Bethe-Salpeter equation |
| 第 10 週 | Coherent States: Bosons |
| 第 11 週 | Coherent States: Grassmann numbers, CS for fermions and spins |
| 第 12 週 | Path integration: Bosons, fermions, spins, connection to Green functions, saddle points, and fluctuations |
| 第 13 週 | Path integration: Hubbard-Stratonovic transformation, Noether theorem, Ward-Takahashi identities |
| 第 14 週 | Fermions in 2 and 3 dimensions: Fermi liquid |
| 第 15 週 | Fermions in 1 dimension: Bosonization |
| 第 16 週 | BCS theory: From electron-phonon to the BCS self-consistency equation |
Negele & Orland: Quantum Many-particle Systems Fetter & Walecka: Quantum Theory of Many-Particle Systems Altland & Simons: Condensed Matter Field Theory Giuliani & Vignale: Quantum Theory of the Electron Liquid
- 時間
- By appointment
- 聯絡方式
- kirchner@nycu.edu.tw