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TA3: Many-Body Physics – Material/Schedule

L1: Tue, 04/25 Introduction, 1) Linear response and generalized susceptibilities (Giamarchi)
L2: Wed, 04/26 generalized susceptibilities, fluctuation dissipation theorem, Kramers-Kronig
L3: Thurs, 04/27 2) 2nd quantization: many-body wave-functions, basics (following Giamarchi)
L4:Tue, 05/02 2nd quantization cont'd: Bogoliubov transformation
L5: Wed,
05/03
2nd quant cont'd.
3) Mean-field theory: General formalism
(Bruus/Flensberg, Chap. 4)
L6: Thurs,
05/04
Mean-field theory cont'd (Hartree-Fock)
T1: Tue
05/09
Linear response
T2, Wed.
05/10
2nd quantization
L7, Thurs.
05/11
Stoner instability, Theory of weakly
interacting Bose gas (Pethick, Smith)
L8, Tues
05/16
Weakly interacting Bose gas cont'd
T3, Wed.
05/17
Mean-field theory: Charge density waves
L9, Thurs
05/18
BCS theory (Pethick, Smith)
L10, Tues
05/23
BCS theory cont'd
T4, Wed.
05/24
Gross-Pitaevskii, MF theory FM Heisenberg
Tues, 05/30 no lecture
T5, Wed.
05/31
Lindhard-function
L11,Thurs, 06/01 4) Fermi-liquids and their instabilities:
Intro & single-particle Green's functions
(following Giamarchi)
T6, Wed.
06/07
BCS theory
L12, Thurs.
06/08
Single-particle Green's fct. cont'd,
Tue, 06/13 Midterm exam
L13:
Wed. 06/14
Quasi-particle life-time from Fermi's golden rule, Fermi-liquid instabilities (following Giamarchi)
L14,
Tue, 06/20
Fermi-liquid instabilities cont'd: nesting, collective modes (following Giamarchi)
T7:
Wed, 06/21
More on Green's functions
L15,
Thu, 06/22
Nesting instabilities con'td.
5) Zero-temperature Green's functions:
single-part. Gs (Bruus/Flensberg Ch. 8)
L16,
Tue, 06/27
Equation of motion (Bruus/Flensberg Ch. 9)
T8,
Wed, 06/28
Photoemission
L17,
Thu, 06/29
examples (level coupled to continuum), derivation of RPA from equation of motions.
L18,
Tue, 07/04
6) Imaginary-time Green's functions (Bruus/Flensberg Chap. 11): Imaginary time, Matsubara Green's functions, relation to retarded Green's function, analytic continuation, single-particle G(τ),
L19,
Wed,07/05
Evaluation of Matsubara sums, equation of motion, Wick's theorem
L20,
Thu, 07/06
Wick's theorem for thermal expectation values and for Matsubara functions
L21,
Tue, 07/11
7) Mott insulator transition, Gutzwiller ansatz for Bose-Hubbard
T9,
Wed, 07/12
More on single-particle Green's functions
T10,
Thurs, 07/13
Matsubara formalism
L22,
Tue, 07/18
From Fermi-Hubbard to Heisenberg model:
Schrieffer-Wolff trafo
T11,
Wed., 07/19
Mean-field phase diagram of the Bose-Hubbard model
L23,
Thu, 07/20
Spin-wave theory for the 2D Heisenberg antiferromagnet
L24,
Tue, 07/25
8) Diagrammatic perturbation theory based on finite-T formalism (Bruss/Flensberg Chaps. 5 & 13)
T12,
Wed.,07/26
Mermin-Wagner theorem
L25,
Thu, 07/27
Feynman diagrams and diagram rules, examples, Dyson eq., self energy, irreducible diagrams

Verantwortlich für den Inhalt: F. Heidrich-Meisner