Università Roma Tre

Ist Part

1 - Homogeneous electron gas in a neutralizing background (jellium model).
Zero order approximation: Sommerfeld theory. Coulombian interaction as perturbation. Hartree-Fock theory for electron gas. Distribution Definition of correlation energy.

2- Second quantization: Fock space for bosons and fermions. Creation and destruction operators. Field operators. Operators in second quantization. The jellium model in second quantization, first order perturbation and comparison with the Hartree-Fock results. Beyond the first order approximation the many body perturbative theory.

3 - The Green Functions for the Electron Gas. Green functions for non-interacting electrons. Lehmann representation.
Perturbative development for Green's functions. Dyson equation. Self-energy.

4 - Polarization propagator. Polarization diagrams. Proper polarization.
Correlation energy in terms of polarization propagator. Random phase approximation (RPA). Dielectric function in RPA. High-density limit, Thomas-Fermi screen. Limit to large wavelengths, plasma oscillations.

5- Introduction to the Density Functional theory for the solid state physics.

2nd Part

1 - The phenomenon of superfluity. The phase diagram of He4. The superfluid phase of liquid helium.
The theory of the two fluids. Landau's theory: critical speed, rotons and phonons.
Bogoliubov's theory of interacting bosons.
Hydrodynamics and vorticity. Vortices as liquid helium excitations.
Recent achievements of Bose-Einstein condensation.

2 - The phenomenon of superconductivity. Zero resistance, Meissner Effect, Critical Magnetic Field,
Specific heat. Analogies with the phenomenon of superfluidity. London equation. Thermodynamic considerations.
Superconductors of the first type and of the second type.

3 - Microscopic theory of superconductivity. Electron-phonon interaction. Attractive interaction between electrons. Cooper pairs. Bardeen-Cooper-Schrieffer's theory (BCS): fundamental state, definition of energy gap. Excited states. Calculation at finite temperature. Quantization of magnetic flux.

4 - Phenomenological theory of Ginzburg-Landau. Landau theory of phase transitions. Free energy of superconductors.
Ginzburg-Landau equations and relation with the London equation.

5 - Symmetry breaking and transition from normal to superconducting state.

A.L.FETTER, J.D.WALECKA "QUANTUM THEORY OF MANY PARTICLES"
G.GROSSO, G.PASTORI-PARRAVICINI "SOLID STATE PHYSICS"