Statistical Physics of Cold Atoms

by A. Trombettoni (5 credits, type B)

Double Well

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
  • 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
  • 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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