*** Notice: links are not maintained after the end of course!
- Science Building 5, Room 633; rshindou@riken.jp
- Office hours: Friday 13:00-15:00
Time and Location
- Wed. 10:10-12:00 & Fri. 8:00-9:50
- Second Teaching Building, Room 412
Requirements
- homework assignment [65%]
- final exam [35%]
References
- Lecture notes
- Statistical Mechanics, R.P. Feynman, ISBN 0-201-36076-4
- Quantum Theory of Many-Particle Systems, Fetter and Walecka, ISBN 0-486-42827-3
- Ming Lu: Science Building 5, Room 606; hiluming@gmail.com
- Lijing Shao: Physics Building, Room S537; Friendshao@gmail.com
Please send an email to quantum-statistical-mechanics-2013-fall+subscribe@googlegroups.com to join the group emaillist!
- You HAVE TO reply the subsequent email received;
- PKU email addresses may be blocked.
Course
Introduction
Quantum Field Theory is an indispensable theoretical tool in modern condensed matter physics. The primary goal of the course is intended to be two-folded; one is to get used to the field-theoretical method of quantum many-particle systems and the other is to study macroscopic quantum phenomena such as superconductivity and superfluidity using the field theory. The course assumes that students are well acquainted to quantum mechanics, statistical mechanics, complex analysis and electromagnetism at the undergraduate level. To make it self-contained, a review on the second quantization is given at the first one or two weeks. In the former part of the course, Green's function approaches to quantum many-particle systems are introduced, where standard Feynman-Dyson perturbation theory in terms of diagrams is developed. In the latter part, the method is applied to several condensed matter systems, such as electron-phonon systems, superconductors and superfluid Helium. One of the most relevant and successful applications of the field-theoretic method in condensed matter physics is the Bardeen-Cooper-Schrieffer (BCS) theory, through which we will study electromagnetic and thermodynamic properties of conventional superconductors. If time allows, we might also have a couple of classes about van der Waals force, collective modes in magnets, and electric resistivity in metals.
Schedule
- 2013-10-09: First class!
- 1.1 general introduction
- 1.2 linear harmonic oscillator
- 1.3 many harmonic oscillators
- 1.4 field quantization
- 2013-10-11
- 1.5 systems of indistinguishable particles; boson and fermion
- 1.6 creation operator and annihilation (destruction) operators
- 1.7 Hamiltonian and other operators in terms of creation and destruction operators
- 2013-10-12: Supplementary class (S1/6) in Room 414, Second Teaching Building!
- 2013-10-16
- 2.2 adiabatic switching and Gell-Mann and Low theorem
- 2013-10-18
- 2013-10-20: Supplementary class (S2/6) in Room 317, Second Teaching Building!
- 2013-10-23
- 2013-10-25
- 2.5 diagramatic analysis of perturbation theory (fermion case)
- 2013-10-26: Supplementary class (S3/6) in Room 414, Second Teaching Building!
- 2.6 (self-consistent) Hartree-Fock approximation
- 2013-10-30
- 2.7 imperfect Fermi gas; dilute gas with short-range interaction, ladder approximation
- Homework 6, 7 (Lijing Shao) [deadline: 2013-11-06]!
- 2013-11-01
- 2013-11-02: Supplementary class (S4/6) in Room 212, Middle Building, School of Physics!
- 2.8 degenerate electron gas; high-density gas with long-range Coulomb interaction
- 2013-11-06
- 2013-11-08
- 3.1 screening effect in degenerate electron gas
- 2013-11-09: Supplementary class (S5/6) in Room 414, Second Teaching Building!
- 2013-11-13
- 3.2 collective modes; plasma oscillation and zero sound mode
- 2013-11-15
- 4.1 temperature (Matsubara) Green's function
- 2013-11-16: Supplementary class (S6/6) in Room 414, Second Teaching Building!
- 4.2 temperature Green's function in the interaction picture
- 2013-11-20
- 4.3 Wick's theorem for temperature Green's function
- 4.4 Feynman Rule for temperature Green's function
- 2013-11-22
- 4.5 Dyson equations and Hartree-Fock approximation
- 4.6 Specific heat of an imperfect Fermi gas at low-temperature
- 2013-11-23: Supplementary class substituting for 2013-11-27 in Room 212, Middle Building, School of Physics!
- 4.7 real-time Green's functions and generalized Lehmann representation
- 2013-11-27: No class; moved to 2013-11-23!
- 2013-11-29
- 4.8 linear response at finite temperature
- 2013-12-04
- 4.9 collective modes at high temperature
- 2013-12-06
- 2013-12-11
- 5.1 non-interacting phonon system and Debye theory of specific heat
- 5.2 electron-phonon interaction
- 2013-12-13
- 5.3 Feynman rule for electron-phonon systems: equivalent electron-electron interaction and BCS Hamiltonian
- 6.1 superconducting properties and thermodynamic relations
- 2013-12-18
- 6.2 BCS theory; Cooper pair, canonical transformation and gap equation
- 2013-12-20
- 2013-12-25
- 6.3 electromagnetic properties of superconductors
- 2013-12-27: Last class!
- 2013-12-30: The STRICT overall homework submission deadline!
- 2014-01-06: 15:00-17:00; office hours for answering questions!
- 2014-01-08: Final exam, beginning from 8:30AM in Room 302, Second Teaching Building! (^_^) Good luck!
Course website maintained by Lijing Shao