Second quantization, Fano model, Hubbard model, Heisenberg model, Crystals and Bloch theorem, Holstein model, Peierls distortion, Polarons.
Contour formulation of time-dependent quantum mechanics.
Martin-Schwinger hierarchy and Wick theorem, Konstantinov-Perel formalism, Keldysh formalism, Matsubara formalism, Zero-temperature formalism.
Feynman diagrams, loop rule, Cancellation of disconnected diagrams, topologically inequivalent diagrams, self-energy and Dyson equation, G-skeleton diagrams, W-skeleton diagrams, Feynman rules in arbitrary basis
Keldysh components and Langreth rules, Kadanoff-Baym equations
Galitskii-Migdal formula, Photoemission theory, Meir-Wingreen formula for quantum transport, fluctuation-dissipation and other exact properties of the Green’s function, spectral function and physical interpretation
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.