Second Quantization Formalism: Second quantization – basic formalism – introduction. Identical fermions – electron gas. Phonons. Basic Concepts and Tools: Canonical transformations. Green s functions. Thermal Green s functions. Path integrals. Symmetries and Symmetry Breaking. Interacting Electrons: Nearly free electrons. Fermi liquid, quasi-particles, Hartree-Fock approximation. Collective excitations (random phase approximation, plasmons, excitons). Nesting properties, low-dimensional systems, Spin and charge density waves, itinerant ferromagnetism. Strongly correlated electrons, Hubbard-type Hamiltonians. Electron-ion interaction (or other bosonic fields): Jellium model, Peierls instability. Frolich Hamiltonian, Polarons. Interaction with spin fluctuations. Macroscopic Quantum States: Bose-Einstein condensates. Superfluidity, Helium 4. Superconductivity, Ginzburg-Landau and BCS Theories. Unconventional Superconductivity in Helium 3. Nambu-Eliashberg theory. Complex Quantum Order States of Matter: Inhomogeneous superconductivity, FFLO states, strong scattering with imperfections, unconventional magnetic order states and charge order states, Pomeranchuk instabilities. Coexistence and competition of quantum order states, unconventional superconductors and magnets. Contemporary problems. From new superconducting and magnetic materials to neutron stars and Laser-trapped fermionic gases.
- Teacher: Γεώργιος Βαρελογιάννης
ECTS : 5
Language : el