| Week 1 | |
| Monday, January 27 | Introductory lecture |
| Wednesday, January 29 | Ch. 1 First and Second Quantization; Landau and Lifshitz Ch. 9
1.1, 1.2 Fermi and Bose exchange symmetry; Many-body wave functions in first quantization; Occupations numbers |
| Friday, January 31 | 1.3 Matrix elements of single-particle operators between many-body wave functions; Creation and destruction operators for bosons |
| Week 2 | |
| Monday, February 3 | 1.3 Psi-operator, second quantization, one-particle and two-particle vertices as Feynman diagrams |
| Wednesday, February 5 | 1.3 Slater determinant; Second quantization for fermions |
| Friday, February 7 | 1.4 Second quantization in momentum representation |
| Week 3 | |
| Monday, February 10 | Guidance for Homework 1
HW 1 issued (Tight-binding models; Coulomb/Yukawa interaction; Jordan-Wigner transformation) |
| Wednesday, February 12 | 2.1 Volume normalization in momentum representation; free Fermi gas; Fermi surface, energy, and momentum |
| Friday, February 14 | UMD campus is closed because of snow |
| Week 4 | |
| Monday, February 17 | 1.5 Occupation numbers at a finite temperature;
brief summary of statistical mechanics;
HW 2 issued (Bogoliubov transformations for fermions, bosons, and 1D spin-1/2 chain) |
| Wednesday, February 19 | Ch. 2 The Electron Gas; 2.2 Comparison of kinetic and Coulomb energies in a 3D electron gas: the Bohr radius, the Rydberg, and the parameter rs |
| Friday, February 21 | 2.2 Direct energy of Coulomb interaction in an electron gas and its cancellation |
| Week 5 | |
| Monday, February 24 | 2.2 Exchange energy of the interacting electron gas; binding energy in liquid Na |
| Wednesday, February 26 | Ch. 3 Phonons; Coupling to Electrons; 3.3 Quantization of lattice vibrations in 1D; phonons |
| Friday, February 28 | 3.3 Acoustical and optical phonons; phonons in 3D |
| Week 6 | |
| Monday, March 3 | UMD campus is closed because of snow.
HW 3 issued (Electron-phonon coupling) |
| Wednesday, March 5 | 3.6 Electron-phonon interaction in the lattice model |
| Friday, March 7 | 1.4.2 Second quantization of electromagnetic field; photons |
| Week 7 | |
| Monday, March 10 | 1.4.3 The current operator; Ch. 4 Mean-Field Theory, 4.1 Basic concepts |
| Wednesday, March 12 | 4.3 Hartree-Fock approximation; Cooper pairing
HW 4 issued (Mean-Field Theory) |
| Friday, March 14 | Problems 1 and 2 of HW 4: Landau theory of a Heisenberg ferromagnet;
Curie and Curie-Weiss susceptibilities; Mean field and feedback mechanism of phase transitions |
| Week 8 | |
| Monday, March 24 | Problem 3 of HW 4: charge-density wave in 1D electron-phonon model |
| Wednesday, March 26 | 4.5.2 Ferromagnetism in the Hubbard/Stoner model in the mean-field approximation |
| Friday, March 28 | 4.5.2 Ferromagnetic instability in the Hubbard model, obtained from divergent susceptibility; Antiferromagnetism of localized spins and itinerant electrons, spin-density wave in the Hubbard model |
| Week 9 | |
| Monday, March 31 | Ch. 5 Time Dependence in Quantum Theory; 5.1-5.3 Schrodinger, Heisenberg and interaction representations; Time-ordered evolution operator |
| Wednesday, April 2 | 5.5 Time evolution of creation and annihilation operators; 5.6 Exponential decay parameter \eta; Fermi's golden rule |
| Friday, April 4 | 5.7 T-matrix and generalized Fermi's golden rule; Unitarity relation between the imaginary part of (i|T|i) and the total transition rate |
| Week 10 | |
| Monday, April 7 | Ch. 6 Linear Response Theory; 6.1 The general Kubo formula;
HW 5 issued (Time Dependence in Quantum Theory) |
| Wednesday, April 9 | Domain of applicability of the Kubo formula; the kinetic equation; 6.1.1 Kubo formula in the frequency domain |
| Friday, April 11 | Ch. 8 Green's Functions; 8.1 "Classical" Green's functions;
Victor Yakovenko is away, substituted by Prof. Jay Sau |
| Week 11 | |
| Monday, April 14 | 8.3 Single-particle Green's function of many-body systems |
| Wednesday, April 16 | 8.3.3 The Lehmann representation |
| Friday, April 18 | 8.3.4 The spectral function for free particles and 8.3.5 its broadening; 8.4.1 Tunneling spectroscopy |
| Week 12 | |
| Monday, April 21 | 8.4.1 Tunneling spectroscopy and its physical interpretation;
HW 6 issued (Green's Functions) |
| Wednesday, April 23 | 6.4 Kubo formula for the dielectric function; 8.5 Two-particle correlation functions of many-body systems |
| Friday, April 25 | 8.5 Two-particle correlation functions of many-body systems |
| Week 13 | |
| Monday, April 28 | 8.5 Imaginary part of the two-particle correlation function;
applications to neutron scattering;
two-particle constraints on due to conservation of energy and momentum Fig. 8.3 |
| Wednesday, April 30 | Ch. 11 Imaginary-time Greene's Functions; Victor Yakovenko is away, substituted by Prof. Jay Sau |
| Friday, May 2 | 11.2 Definition of Matsubara Green's function;
11.1.1 Fourier transform of Matsubara Green's function;
11.2 Connection between Matsubara and retarded functions |
| Week 14 | |
| Monday, May 5 | 11.3 Single-particle Matsubara Green's functions;
11.4 Evaluation of Matsubara sums;
HW 7 issued (Imaginary-time Green's Functions) |
| Wednesday, May 7 | 11.5 Equations of motion; 11.6 Wick's theorem |
| Friday, May 9 | 11.7 Polarizability of free electrons |
| Week 15 | |
| Monday, May 12
update point |
Ch. 13 Feynman Diagrams and Pair Potentials;
13.1 The perturbation series for Green's function G;
13.2 The Feynman rules for pair interactions; 13.3 Self-energy and Dyson's equation; 13.5 Cancellation of disconnected diagrams; HW 8 issued (CDW instability in 1D and Q1D interacting electron gas) |
| Final Exam | |
| Monday, May 19, 8-10 am | Submit Homework 8 as a take-home exam;
Make-up lecture for two snow days:
Ch. 14 The Interacting Electron Gas; Ch. 18 Superconductivity |
Last updated May 17, 2014