Teoria dei solidi 2010-11
Program
1)Intraduction:Landau Fermi liquids, Mott transition, Ginzburg-Landau theory of phase transitions. Magnetism: mean field –Ising model : Exact solutions . Renormalization approach, Hubbard-Stratonovich transformation
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2) Fano resonances. Anderson model. Newns model of chemisorptions. Kondo effect. Esca. Lunqvist model.Inverse Photoemission. Auger Spectroscopy: Cini-Sawatzky theory and extensions , APECS. One Step Model. Low-density methods applied to the spectra of transition metals. Hubbard model and magnetism (Lieb theorems, Nagaoka ferromagnetism)
3)Recursion approaches: Lanczos method, method of excitation Amplitudes, Spin disentangled approach, Howard Lee recurrants.
4) Group representations. Great Orthogonality Theorem. Orthogonality of Characters. Applications to orbitals and vibrations in solids. Space-time symmetries of Bloch states. Space Groups . Young diagrams . Direct product. Double Groups. Jahn-Teller effects. Vibronic Coupling.
5)Quantum phases- Berry phase, molecular Aharonov-Bohm effect and polarization of solids.
6) W=0 pairing in the Hubbard Model and Cuprate Superconductivity.
7)Low-dimensional physics: Bethe ansatz for 1d Heisenberg model. Nanotubes. Bosonization and spin-charge separation. Quantum Hall effect.
8)More on Green’s functions methods: Inglesfield embedding. Conserving approximations. Ward Identity. Equations of Motion. Keldysh time-dependent theory.
9) Quantum transport. Landauer formula. Time dependent formulation of quantum transport. Magnetic moments of Quantum rings-Transport in Graphene.
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