quantum mechanics, solid state physics, statistical physics

TTK Fizikus MSc képzés Kutató fizikus specializáció kötelezően választható tárgya

The course introduces the Green's function technique to investigate interacting electronic systems, mostly within the context of solid state physics. The course relies on the knowledge of basic quantum mechanics and statistical physics and is practically essential for other courses such as Many-body theory 2, Physics of one dimensional systems, Disordered systems etc. During the semester, the following topics are discussed:

- Second quantization, definition of Green's functions and their relations to physical quantities
- Heisenberg, Schrödinger and interaction pictures
- Perturbation theory, diagrammatics (Wick's theorem, Feynman diagrams), resummations (self energy, vertex function, skeleton diagrams), equation of motion method
- Having acquainted with the technique, we use it to evaluate
- The ground state energy of dense, interacting electron gas
- Friedel oscillations around a charged impurity
- Anderson's orthogonality catastrophe and Fermi edge singularity
- RKKY interaction between localized magnetic moments
- Mean-field theory of two dimensional antiferromagnets etc.

The corresponding practical course offers a variety of related problems to be solved.

G.D. Mahan: Many-Particle Physics (Plenum Press, New York and London, 1981)

A.A. Abrikosov, L.P. Gorkov and I. Dzialoshinskii: Methods of Quantum Field Theory in Statistical Mechanics (1963)

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Dr. Szunyogh László