Olivier Parcollet (IPhT, CEA Saclay)

Methods for quantum many body problems out of equilibrium (10 h)

1. Basic theoretical concepts for quantum many body systems

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.

2. Quantum impurity models

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.