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A. Many-Body Methods
- Introduction: Spontaneous Symmetry Breaking
- Handouts (see Spontaneous Symmetry Breaking)
- Free-electron Gas
- Tight-binding
- Born-Oppenheimer Approximation
- 2nd Quantization and Field Operators
- Hartree States/Hartree-Fock Approximation/Koopmans Theorem
- Interacting Electron Gas
- Beyond H.F./Wigner Interpolation
B. General Many-Body Phenomena
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C. Superconductivity
- General Properties of Type I and Type II Superconductors
- London Equations
- Handouts (see Weinberg's paper on superconductivity)
- Handouts (see Fractional Electro-magnetism)
- Energy Gap, Penetation Depth, Ultrasonic Attenuation
- NMR (Hebel-Slichter Peak)
- BCS Model
a. Phonon-induced Cooper Pair
Formation
b. Global Pair State
c. Normal Ground State Instability
d. Gap Equation
e. Quasi-particle Excitations
f. Thermodynamics
g. Nuclear Spin-lattice Relaxation
D. Localization and Quantum Hall physics
- Anderson Localization
- Weak Localization
- Integer Quantum Hall Effect
- Topological Insulators
- Fractional Quantum Hall Effect
E. Mott physics
1. Mott insulators: Mottness
2. Hubbard Model
3. Antiferromagnetism
4. Hatsugai-Khomoto Model
F. Course Requirements
- Five Homework Sets (approximately) (1/3 of grade)
- Take-home midterm (1/3 of grade)
- Take-home Final (1/3 of grade)
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