# PřF:FK110 Diagram. meth. in solid state - Course Information

## FK110 Diagrammatic methods in modern condensed matter physics

**Faculty of Science**

Autumn 2024

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
**Guaranteed by**- prof. Mgr. Dominik Munzar, Dr.

Department of Condensed Matter Physics – Physics Section – Faculty of Science

Contact Person: doc. Mgr. Jiří Chaloupka, Ph.D.

Supplier department: Department of Condensed Matter Physics – Physics Section – Faculty of Science **Timetable**- Mon 15:00–17:50 Fs2 6/4003
**Course Enrolment Limitations**- The course is offered to students of any study field.
**Course objectives**- Fundamentals of propagators-based description of interacting many particle systems.
**Learning outcomes**- At the end of the course students should understand the concept of Green's function, its relation to observable quantities, apply it in interpreting experimental data, express the Green's functions of interacting many particle systems in terms of Feynman diagrams and solve simple related problems.
**Syllabus**- 1. Green's functions and propagators in classical physics and in single-particle Quantum mechanics.
- 2. Simple example - single electron in a crystal lattice with an impurity atom.
- 3. Reminder: Second quantization formalism and statistical description of quantum many particle systems.
- 4. Propagators: definion, formal properties, spectral representation etc., examples: non-interacting electron gas, Anderson impurity model, Matsubara propagators.
- 5. Computations of amplitudes using diagrammatic perturbation theory, Dyson's series, Wick theorem, Feynman diagrams.
- 6. Noninteracting electron gas: linear response theory, Kubo formula, Linhard theory etc.
- 7. Electron gas with Coulomb interaction: Hartree-Fock approximation, screening, RPA approximation, plasmons, Landau damping, GW theory.
- 8. Itinerant electron magnetism: Hubbard model, RPA spin susceptibility, magnetic instability and criticial behaviour in its proximity.
- 9. Interacting electron-phonon system: lattice vibration and the free phonon propagator, electron-phonon coupling and its manifestations.
- 10. Propagators in the BCS theory of superconductivity.

**Literature**- G. Rickayzen: Green's Functions and Cond. Matter, Dover Publications, New York, 2013
- S. Doniach a E. H. Sondheimer: Green's Functions for Solid State Physicists, Imperial College Press, London, 1998
- G. D. Mahan: Many-Particle Physics, Kluwer Academic/Plenum Publishers, New York, 2000
- A.A. Abrikosov, L. P. Gorkov a I.E. Dzyaloshinski: Methods of Quantum Field Theory in Statistical Physics, Dover Publications, New York, 1975

**Teaching methods**- Lectures, where the topics are introduced, seminars, where solutions of related problems are presented and discussed.
**Assessment methods**- Exam. As part of the home preparation for the oral exam, several complex problems are assigned. The exam then takes the form of a discussion of the student's solutions and of the course topics in general. The final evaluation reflects the level of understanding.
**Language of instruction**- Czech
**Teacher's information**- https://www.physics.muni.cz/~chaloupka/FK110/

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2024/FK110