Green functions and diagrammatic perturbation theory. Matsubara formalism.
Baym-Kadanoff-Luttinger-Ward functional. Scattering theory; Fermi liquid.
Schwinger-Keldysh perturbation theory; illustration on simple cases; introduction to quantum Boltzmann equation.
Introduction to Anderson and Kondo models; 1d formulation. Kondo model in quantum dots; Coulomb blockade.
Kondo temperature; local Fermi liquid; Abrikosov-Suhl resonance; screening of the impurity; slave boson approximation; renormalization group approach; Non Crossing Approximation (NCA).
Generalized models; non-Fermi liquid fixed points.
Quantum impurity out of equilibrium. Introduction to multiple impurity models. Algorithms to solve quantum impurity models in and out of equilibrium : Monte-Carlo algorithms, Renormalization Group approaches.
An introduction to Dynamical Mean Field Theory.