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Course, academic year 2018/2019
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Statistical Physics of Quantum Many-particle Systems I - NTMF031
Title in English: Statistická fyzika kvantových mnohočásticových systémů I
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://otokar.troja.mff.cuni.cz/vyuka/sylaby/sylaby.htm
Guarantor: prof. RNDr. Václav Janiš, DrSc.
Classification: Physics > Theoretical and Math. Physics
Is co-requisite for: NTMF032
Annotation -
Last update: prof. RNDr. Jiří Podolský, CSc., DSc. (29.04.2019)
Quantum statistical mechanics, second quantization and Fock space, ideal and non-ideal quantum gases, two-particle interaction. Perturbation theory for interacting systems, Matsubara's formalism, analytic properties of perturbation series and of Green's function. Feynman diagrams, Dyson and Bethe-Salpeter equations, Ward identities and simple approximations. Interacting electrons in metals, microscopic basis of the Fermi liquid theory. For the 4th and 5th year of the TF and FPL studies and for doctoral students.
Literature - Czech
Last update: prof. RNDr. Václav Janiš, DrSc. (11.10.2017)

G. D. Mahan, Many-Particle Physics, Plenum Press, New York 1990.

Ch. Enz: A course of many-body Theory Applied to Solid State Physics, Spúringer-Verlag, Berlin 1982.

J. W. Negele, H. Orland, Quantum Many-Particle Physics, Addison-Wesley Publishing House, Redwood City, 1988.

W. Nolting: Viel-Teilchen Theorie, Springer-Verlag, Berlin 2015.

Requirements to the exam - Czech
Last update: prof. RNDr. Václav Janiš, DrSc. (11.10.2017)

Zkouška je ústní. Každý student dostane tři otázky, z nichž jedna je početního charakteru, aby student prokázal zvládnutí použitý naučeného formalismu. Požadavky ke zkoušce se kryjí se sylabem a dostupným skriptem s omezením na skutečně probranou látku v kursu. K získání zkoušky je třeba zvládnout početní otázku a alespoň jednu metodickou otázku.

Syllabus -
Last update: prof. RNDr. Václav Janiš, DrSc. (11.10.2017)

Nonrelativistic quantum dynamics, Fock space and second quantization; interacting fermions, bosons; model Hamiltonians of interacting systems in solid state theories: electron-electron and electron-phonon interaction.

Interaction representation, S-matrix, Green functions, Wick theorems; Feynman diagrams, self-energy and Dyson equation, polarisation operator and vertex functions.

Perturbation theory for non-zero temperatures, Matsubara frequencies; cluster expansion for the thermodynamic potential; analytic properties of Green functions and frequency summations, linked-cluster theorem.

Time-dependent Green functions at non-zero temperatures, Keldysh-Schwinger formalism.

Graphical representation of the perturbation expansion, Feynman diagrams and their classification, renormalization of the perturbation expansion.

 
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