-Group theory with condensed-matter applications (orbitals, vibrations, spin, Jahn-Teller –effect, symmorphic and not symmorphic lattices –magnetic crystals– electron states in solids).
- Lippmann-Schwinger equation
– Fano and Anderson models
- Kondo singularity
- Kubo linear response formalism
- Lehmann representation
– Two-hole Risonances and Cini-Sawatzky theory of Auger spectra
– Feynman diagrams
– Herglotz property- Bethe-Salpeter equation
–Applications of the diagram method: high and low density cases.
– Hedin equations –conserving approximations
– Density Functional theory.
- Ward identity-Recursion, renormalization and numerical methods with examples.
-Basic ideas about Magnetis
- Hubbard Model
- Berry phase and the theory of polarization of solids.
– Quantum Hall effects and other topology
– Quantum transport and pumping.
LEARNING OUTCOMES: Provide an introduction to the theory of quantum systems with many interacting particles in order to calculate equilibrium properties as well as linear and nonlinear responses. The main investigation tool is the non-equilibrium Green's function theory useful in many applications of modern condensed matter theory.
KNOWLEDGE AND UNDERSTANDING: Students must have an in-depth understanding of the theoretical methods developed, the derivation of the most important results and the connection with some modern experimental investigation techniques
APPLYING KNOWLEDGE AND UNDERSTANDING: Students must be able to model or introduce appropriate approximations for the study of a complex physical problem.
MAKING JUDGEMENTS: Students must be able to carry out complex calculations independently and must develop a critical approach to existing theories in order to identify their domain of applicability and understand how to correct them.
COMMUNICATION SKILLS: Students must be able to illustrate a topic clearly and concisely, highlighting the physical problem and the idea that leads to its solution.
LEARNING SKILLS: Students must be able to understand modern review articles on topics related to the program of the course.