統計場論與量子相變

Phase transitions are broad and generic phenomenon in many-body systems where the state of matter transforms from one to the other with the change of external parameters. This course is the introduction to phase transitions in statistical mechanics. The classical phase transitions are driven by thermal fluctuations, while the quantum phase transitions are driven by quantum fluctuations. Near the transitions, physical observables show universal power-law scaling. Critical phenomena in various physical systems are discussed. Statistical field theory based on Landau-Ginsburg theory is used to describe these phase transitions. The goal of this course is to give students a modern introductory understanding in classical and quantum phase transitions as well as critical phenomenon via field theory approach.

Solid state physics I, II, Advanced Solid State Physics I,II Quantum Mechanics I,II

TA available to grade HWs, provide solutions on the NCTU-e3 website.

作業部份: There will be homework every week. 考試部份: No mid-term exam. There will be a final take-home exam. 評量部份: 70% Homework 30% Final exam

• Introduction to phase transitions
• How phase transitions occur in principle I
• How phase transitions occur in principle II
• *How phase transitions occur in practice (Ising model)
• Landau-Ginsburg theory of phase transitions
• Fluctuations and the breakdown of the Landau theory
• Scaling hypothesis and relations
• The renormalization group (RG)
• Continuous symmetry and Kosterlitz-Thouless transition
• Critical phenomena near four dimensions
• Introduction to quantum phase transitions
• Quantum rotor model at T=0
• Quantum rotor model at finite temperatures
• *Physics close to upper critical dimension

1.Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992 2.Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.

地點

SC453

時間

Office hours: Mon. 2:00pm-3:00pm Wed. 2:00pm-3:00pm Fri. 2:00pm-3:00pm

聯絡方式

chung@mail.nctu.edu.tw Tel: 03-5712121#56107