高等固態物理(二)

This course is the advanced solid state theory. The important fundamental techniques in quantum many-body theory are introduced, such as: Green's functions, Perturbation theory, Diagramatic expansions, Linear response theory. The goal is to set up the theoretical fundations for graduate students to study more advanced topics in modern solid state physics.

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

無備註

Lecture notes will be available on NCTU open course website.

作業部份: There will be homeworks every 2 to 3 weeks. 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 Green's function

  General introduction to Green's function and its applications to solid state experiments.

  講授：

  3

• * Free particle Green's functions

  Introduce free particle Green's function

  講授：

  3

• Finite temperature Green's functions

  Introduce finite temperature Green's functions

  講授：

  6

• Linear response theory, Masubara formulation

  Introduce linear response theory and Masubara formulism together with Green's functions in calculating transport properties of solids

  講授：

  4

• perturbation theory

  Introduce Perturbation theory, Feynman diagrams and Wick's theorem

  講授：

  6

• *Self-energy

  Introduce how to calculate self-energy corrections in many-body systems

  講授：

  3

• Vertex corrections

  Learn the vertex correction part

  講授：

  3

• Dyson's equations

  This is the approach which can solve self energy and vertex corrections at the same time.

  講授：

  4

• Disorder and localization

  Apply the above Green's function techniques to a specific quantum many-body system--Anderson localization in solids with impurities/disorder

  講授：

  6

• Strongly correlated electron systems

  Apply Green's function techniques to the 2nd quantum many-body system-- strongly correlated electron systems. Introduce Hubbard, Heisenberg, and t-J models. Explain magnetic quantum phases and high-Tc superconductivity in cuprates.

  講授：

  9

• Kondo effect in quantum impurity systems

  Apply Green's function techniques to another strongly correlated system--Kondo system. Explain magnetic properties in metals with impurities. Discuss Kondo effect in quantum dots

  講授：

  6

• Introduction to Renormalization Group technique in many-body system

  Give a general introduction to renormalization group theory in quantum many-body systems via Green's function approach.

  講授：

  6

1. Many-body Quantum Theory in Condensed Matter Physics: an introduction, Henrik Bruus and Karsten Flensberg, Oxford University Press, 2004. 2.Green's functions for solid state physicists, S. Doniach and E.H. Sondeheimer, Imperial College Press, 1998 3.Quantum Theory of Many-Particle Systems, A. Fetter and J. Walecka, McGraw-Hill, Inc. 1971 4. Quantum Many-particle systems, J. W. Negele and H. Orland, Addison-Wesley Publishing Company, 1988 5. Interacting Electrons and Quantum Magnetism, Assa Auerbach, Springer-Verlag, 1994.

地點

Engineering buliding #6, EF357

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: X56107