by A. Trombettoni (4 credits)
This course provides an introduction to the area of phenomena emerging from cold atom physics.
Main Topics
Part I
- Condensation for an ideal gas of bosons
- Effects of the interaction: qualitative considerations
- Bogoliubov theory of the weakly interacting Bose gas (WIBG) (and reminders of second quantization)
- Path integral study of the WIBG
- Condensate dynamics at T=0: collective oscillations
- BEC in a double well potential: Josephson oscillations, analogy with
superconducting Josephson junctions - BEC in optical lattices
- BEC in a rotating container: superfluidity, vortices, analogy with the
superfluid Helium - Equilibrium properties of bosons in periodic potentials: Bose-Hubbard
model - Kosterlitz-Thouless transition in 2D
- Ultracold fermions: results for the non-interacting limit
- BCS theory for attractively interacting Fermi gases
Part II
- Introduction to superconductors: basic phenomena
- Electrodynamics of superconductors: London equations, type-II
superconductors - Ginzburg-Landau theory
- BCS-BEC crossover for dilute fermions
- Fermions in optical lattices: Hubbard models
- Green’s function approach to superconductivity and superfluidity: an introduction
