Statistical Physics of Cold Atoms

by A. Trombettoni (3 credits)


Double Well


This course provides an introduction to the area of phenomena emerging from cold atom physics.

Main Topics

I Part

  • 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

II Part

  • 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

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