Teaching	E-mail

Chung-Yu Mou

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