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Teaching |
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E-mail |
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Chung-Yu Mou
Statistical Mechanics (II) |
統計力學
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Fall 2012 |
牟中瑜 |
Syllabus |
授課大綱 |
助教:
游至仕
email: jhihshihyou@gmail.com
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目標
本課程為統計力學 (I) 之延續, 將探討比較深的概念,
以介紹基本的統計模型,相變,尺度不變, 重整化群等多體統計概念為主.
- Introduction to phase transitions
- Basic concepts: phenomenon of phase transitions, Yang-Lee scenario of phase transitions,
broken ergodicity,
broken symmetry and concept of universality
- The Ising models
- Exact solutions for 1D Ising model
- Low temperature expansion
- The Mermin & Wagner theorem
- Results for 2D Ising model
- Mean field theories and the Ginzburg-Landau theory
- Effects of fluctuations
- Gaussian integrals, functional integral in
many-particle theory and perturbative RG analysis
- Introduction to Renormalization Group theory
- RG analysis of 1D Ising model
- Scaling hypothesis and scaling laws
- Origin of universality
- Anomalous dimensions and epsilon expansion
- The Kosterlitz and Thouless transition (RG analysis
and other generalizations such as 2D melting)
- Second quantization and phonons
- Introduction to superfluidity
- Structure factor in liquids and gases
- Virial expansion and the linked cluster theorem
- Reviews of the Bose-Einstein condensation
- Phenomenon of superfluidity
- Bogoliubov theory of the weakly
interacting Bose gas
- The Feynman theory of excitation curve
- Introduction to superconductivity
- Ginzburg-Landau theory
- The BCS theory
- Rudiments of Conformal Field Theory
- Conformal Invariance in 2D
- Virasoro Algebra and Central Charge
- Finite-Size Scaling of the Free Energy
- Zamolodchikov’s c-theorem
- Representation Theory of the Virasoro Algebra
Textbooks and references
- Statistical Mechanics, 2nd edition, by Kerson Huang
- Statistical Mechanics, by R. P. Feynman
- Equilibrium Statistical Physics, 2nd edition, by Michael Plischke and
Birger Bergersen
- Statistical Mechanics, by R. K. Pathria
- Statistical phyiscs part I, by Landau & Lifshitz