Inhaltsbereich
TMPTA6 many body physics (SoSe 2011) – Lecture
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 GF116: Motivation, thermal averaging, Schrödinger, Heisenberg Interaction pictures, timeordering operators, imaginary time  
06.05.11  GF1723': Thermal GF, Periodicity in imaginary time direction, Matsubara transformation  
10.05.11  Kubo formula (O. Yevtushenko)  
13.05.11  GF2436: 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  GF3742, (GF4347 nonexistant), GF4853: Spectral representations, relation between Matsubara and retarded/advanced via analytic continuation in frequency domain, interpretation of spectral function, spectral sum rules 

20.05.11  GF5468: complex conjugation, obtaining retarded/advanced from Matsubara by analytic continuation in time domain, expressing G>, G< in terms of spectral function, fluctuationdissipation theorem, conditions for analytic continuation from G(i omega_n) to G^{R/A}(w +/ i0), Matsubara sums 

24.05.11  Perturbation Theory PT18: Singleparticle potential, equations of motion, Dyson equation, diagrammatic rules, definition of interaction term  
27.05.11  PT915: Expectation value of H in terms of spectral function, interaction picture in imaginarytime domain, definition of npoint correlators, their periodicity properties, translational invariance in time implies frequency conservation 

31.05.11  PT1629: 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  PT3037: Diagrammatic perturbation theory: partition function, 1point function, Feynman rules  
07.06.11  PT3851: 2nd order diagrams, connected diagrams, combinatorical factors, twopoint functions, transforming to momentum and frequency representation, Hartree and Fock diagrams, translational invariance in time and space, Feynman rules  
07.06.11  PT5257: Dyson equation, selfenergy, quasiparticle weight and lifetime, HartreeFock approximation, twoparticle connected diagram  
17.06.11  PT5864: HartreeFock wavefunctions, densityresponse to external potential  
21.06.11  PT6574: Screening of external potential, RandomPhase Approximation, polarization bubble, Lindhardt formula, plasma resonance, ThomasFermi screening length 

21.06.11  Dis113: Disorder potential, selfaveraging, impurity averages, Feynman rule for disorder averaging, 1particle GF, elastic scattering time  
24.06.11  Dis1425: Disordered systems: Higher order diagrams  
28.06.11  Dis2632: Disordered systems: Conductivity before disorder averaging  
01.07.11  Dis3341: Disordered systems: Conductivity after disorder averaging  
05.07.11  Cancellation of diamagnetic term (using identity derived by gauge transformation)  
08.07.11  K07: Kondo Model, poor man scaling  
12.07.11  AM113Anderson model, multilevel dots, SchriefferWolff transformation  
15.07.11  Numerics: NRG, DMRG and Matrix Product States  
19.07.11  Superconductivity: p. 16: Basic properties, electronphonon interaction, phononmediated attraction, Cooper instability  
22.07.11  Superconductivity: p. 714: Properties of the vertex function, critical temperature, statistical approach, anomalous Green's functions  
25.07.11  Superconductivity: p. 1519: Gorkov's equations, reduced BCS model, spectrum of excitations, wavefunction of condensate  
29.07.11  Superconductivity: Matrix Green's functions of Nambu, DoS of excitations, gap equation, Tdependence 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 (lifetimes, 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 finetune your preparations on the last day before the exam. 

08.08.11  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  HartreeFock 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 