| Date | Notes | Subject | |
| Introduction to Second Quantization: Chapter 2.1, A. Altland and B. Simon, "Condensed Matter Field Theory" (2006). | |||
| Appendix C. Second Quantization: M. P. Marder, "Condensed Matter Physics" (2000). | |||
| 03.05.11 |
Green's Functions GF1-16: Motivation, thermal averaging, Schrödinger, Heisenberg Interaction pictures, time-ordering operators, imaginary time | ||
| 06.05.11 |
GF17-23': Thermal GF, Periodicity in imaginary time direction, Matsubara transformation | ||
| 10.05.11 |
Kubo formula (O. Yevtushenko) | ||
| 13.05.11 |
GF24-36: Kubo Formula, definitions of G<, G>, retarded/advanced/causal GF, when is analytic continuation allowed?, periodicity in complex time direction, relation between thermal and causal GF by analytic continuation | ||
| 17.05.11 |
GF37-42, (GF43-47 nonexistant), GF48-53: Spectral representations, relation between Matsubara and retarded/advanced via analytic continuation in frequency domain, interpretation of spectral function, spectral sum rules | ||
| 20.05.11 |
GF54-68: complex conjugation, obtaining retarded/advanced from Matsubara by analytic continuation in time domain, expressing G>, G< in terms of spectral function, fluctuation-dissipation theorem, conditions for analytic continuation from G(i omega_n) to G^{R/A}(w +/- i0), Matsubara sums | ||
| 24.05.11 |
Perturbation Theory PT1-8: Single-particle potential, equations of motion, Dyson equation, diagrammatic rules, definition of interaction term | ||
| 27.05.11 |
PT9-15: Expectation value of H in terms of spectral function, interaction picture in imaginary-time domain, definition of n-point correlators, their periodicity properties, translational invariance in time implies frequency conservation | ||
| 31.05.11 |
PT16-29: Wick's theorem for thermal averages proved by cyclic permutations under trace, Wick's theorem for thermal GF, proved from previous result, and proved using equations of motion | ||
| 03.06.11 |
PT30-37: Diagrammatic perturbation theory: partition function, 1-point function, Feynman rules | ||
| 07.06.11 |
PT38-51: 2nd order diagrams, connected diagrams, combinatorical factors, two-point functions, transforming to momentum and frequency representation, Hartree and Fock diagrams, translational invariance in time and space, Feynman rules | ||
| 7.06.11 |
PT52-57: Dyson equation, self-energy, quasiparticle weight and lifetime, Hartree-Fock approximation, two-particle connected diagram | ||
| 14.06.11 |
Public holiday (Pfingstdienstag) | ||
| 17.06.11 |
PT58-64: Hartree-Fock wavefunctions, density-response to external potential | ||
| 21.06.11 |
PT65-74: Screening of external potential, Random-Phase Approximation, polarization bubble, Lindhardt formula, plasma resonance, Thomas-Fermi screening length | ||
| 21.06.11 |
Dis1-13: Disorder potential, self-averaging, impurity averages, Feynman rule for disorder averaging, 1-particle GF, elastic scattering time | ||
| 24.06.11 |
Dis14-25: Disordered systems: Higher order diagrams | ||
| 28.06.11 |
Dis26-32: Disordered systems: Conductivity before disorder averaging | ||
| 01.07.11 |
Dis33-41: Disordered systems: Conductivity after disorder averaging | ||
| 05.07.11 |
Cancellation of diamagnetic term (using identity derived by gauge transformation) | ||
| 08.07.11 |
K0-7: Kondo Model, poor man scaling | ||
| 12.07.11 |
AM1-13Anderson model, multi-level dots, Schrieffer-Wolff transformation | ||
| 15.07.11 |
Numerics: NRG, DMRG and Matrix Product States | ||
| 19.07.11 |
Superconductivity: p. 1-6: Basic properties, electron-phonon interaction, phonon-mediated attraction, Cooper instability | ||
| 22.07.11 |
Superconductivity: p. 7-14: Properties of the vertex function, critical temperature, statistical approach, anomalous Green's functions | ||
| 25.07.11 |
Superconductivity: p. 15-19: Gorkov's equations, reduced BCS model, spectrum of excitations, wave-function of condensate | ||
| 29.07.11 |
Superconductivity: Matrix Green's functions of Nambu, DoS of excitations, gap equation, T-dependence of gap, Anderson theorem | ||
| 25.07.11 |
Remarks about the exam (Tuesday, August 9, from 10:00 - 13:00, Room 348/349) You can bring along any material (books, lecture notes) you want. The exam will attempt to test both your understanding of the material covered in lectures & excercises and your fluency with the basic calculational tools developed during the course. However, due to the limited time available, no very long calculations will be required. For example, if you are asked to evaluate a Matsubara sum, this will be doable in a few lines (if you know what to do!) Typical questions could involve, for example: - doing the bosonic version of a problem for which the fermionic case was done in lecture or tutorial, or vice versa; - discussing a specific example of a problem or theorem that was discussed in full generality in lecture or tutorial; - writing down and evaluating the algebraic expression associated with a given Feynman diagram (including explaining the combinatiorial factor, if any); - discussing the physical interpretation of a given diagram; - extracting physical quantities (life-times, dispersion relation of excitations) from a given diagram and/or the corresponding correlation function; - explaining the justification for (and/or limitations of) certain "standard" approximation schemes; - ... A more explicit set of hints will be published on this website on Monday morning, August 8, by 9:00 am, to help you to fine-tune your preparations on the last day before the exam. |
08.08.11 |
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More detailed hints: the following topics will feature in the exam: - formal properties of quantum fields, thermal, retarded, advanced Green's functions - know how to do Matsubara sums in detail, including ones involving Green's functions with higher order poles - understand calculation of charge susceptibility in great detail; exam will contain an analogous calculation of a different physical quantity - Hartree-Fock theory - Feynman rules for disordered systems, which diagrams matter for calculation of electron lifetime, which don't, why not? - Kondo problem, poor man scaling, derivation of RG equation - Superconductivity: Gorkov equations, density of states, gap equation, calculation of Delta(T=0), Tc |