The course presents theories and methods for the study of ground state excited properties in many electron systems.In particular:
Mean field theories for the computation of electronic states in materials; single particle approximations and beyond. Density functional theory and its computational implementation. Many-body theory of excitonic states. Plasmon theory and dielectric screen in crystals. Projected density of states and Green's function. Moments of a Hamiltonian and Green's function. The classical problem of moments and its solution with continued fractions. The recursive method of Haydock-Heine-Kelly-Lanczos. Dyson equation and renormalization method for electronic states. Construction of tight-binding reduced Hamiltonians for the computation of electronic states in multilayer systems. Recursive methods and electronic transport. Superconductivity: phenomenological aspects, thermodynamic theories, London theory, Pippard theory, Ginzburg-Landau theory. Electron-electron interaction mediated by phonons; BCS theory, Bogoliubov-Valatin theory, Tunneling Giaever and tunneling Josephson. Andreev's reflection.