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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
|
Fall 1999 |
牟中瑜 |
Syllabus |
授課大綱 |
目標
本課程為統計力學 (I) 之延續, 將探討比較深的概念.
- 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 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)
- Introduction to superfluidity
- Structure factor in liquids and gases
- Virial expansion and the linked cluster theorem
- Reviews of the Bose-Einstein condensation
- Introduction to the Bose-Einstein condensation in cold
atoms
- Phenomenon of superfluidity
- The Feynman theory of excitation curve
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