Statistical Physics of Quantum Many-particle Systems II - NTMF032
Title: Statistická fyzika kvantových mnohočásticových systémů II
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Václav Janiš, DrSc.
Classification: Physics > Theoretical and Math. Physics
Co-requisite : NTMF031
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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.
Course completion requirements -
Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2023)

Oral exam

Literature -
Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2023)

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 -
Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2023)

The exam is oral. Each student is given three questions, one of which is practical to demonstrate mastery of the learned formalism. The exam requirements are in the syllabus, limited to the material actually covered in the course. To pass the exam, you need to pass the practical question and at least one theoretical question.

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.