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Course, academic year 2017/2018
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Statistical Physics of Quantum Many-particle Systems II - NTMF032
Czech title: Statistická fyzika kvantových mnohočásticových systémů II
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer 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
Co-requisite : NTMF031
Annotation -
Last update: T_UTF (25.04.2003)

Strongly interacting particles, lattice models, electron-electron and electron-phonon interaction. Self-consistent approximations for strongly correlated electrons: functional integral and saddle-point method, static approximation, the mean-field method and the limit of large dimensions. Quantum dynamical phenomena: Kondo effect and the formation of local magnetic moments, theory of magnetism in transition metals. Microscopic theory of superconductivity. Exactly solvable models - Bethe ansatz for correlated electrons. The course follows TMF031.
Literature - Czech
Last update: prof. RNDr. Václav Janiš, DrSc. (11.10.2017)

G. Rickayzen: Green's Functions and Condensed Matter, Academic Press, London 1984.

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

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

A. M. Zagoskin: Quantum Theory of Many-Body Theory Applied to Solid-State Physics, World Scientific, Singapore 1992.

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)

Simple approximations of correlated electron systems, Hartree-Fock approximation, T-Matrix, Random Phase approximation, Schwinger-Dyson and Bethe-Salpeter equations, Ward identities, parquet equations.

Linear-response theory, Kuba formula, Kramers-Kronig relations and dissipation-fluctuation theorem; electrical conductivity.

Landau theory of Fermi liquid; quasi-particles and their interaction, normal Fermi liquid, equilibrium and non-equilibrium properties; microscopic motivation, Landau parameters.

Theory of superconductivity; electron-phonon interaction and Cooper instability, BCS theory of superconductivity, Nambu formalism, ordering parameter and thermodynamics of superconductors; electron tunneling and Josephson's phenomenon.

 
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