Syllabus
Simple approximations of correlated electron systems, Hartree-Fock approximation, T-Matrix, Random Phase approximation, Schwinger-Dyson and Bethe-Salpeter equations, Ward identities, parquet equations.
Linear-response theory, Kuba formula, Kramers-Kronig relations and dissipation-fluctuation theorem; electrical conductivity.
Landau theory of Fermi liquid; quasi-particles and their interaction, normal Fermi liquid, equilibrium and non-equilibrium properties; microscopic motivation, Landau parameters.
Theory of superconductivity; electron-phonon interaction and Cooper instability, BCS theory of superconductivity, Nambu formalism, ordering parameter and thermodynamics of superconductors; electron tunneling and Josephson's phenomenon.
Annotation
Strongly interacting particles, lattice models, electron-electron and electron-phonon interaction. Self-consistent approximations for strongly correlated electrons: functional integral and saddle-point method, static approximation, the mean-field method and the limit of large dimensions.
Quantum dynamical phenomena: Kondo effect and the formation of local magnetic moments, theory of magnetism in transition metals. Microscopic theory of superconductivity.
Exactly solvable models - Bethe ansatz for correlated electrons. The course follows TMF031.