Bosonic Physics

Mike Gunn

  • Introduction: phenomena in 4He and bose condensed atoms in traps as paradigms, an F = U -TS treatment of the ideal bose gas, why it is deficient in terms of critical velocities (Landau criterion) and the excitation spectrum by appeal to experiment – interactions are needed.
  • Derivation of inviscid fluid dynamics from a mean field treatment of the interacting problem, introducing the number-phase variables. Vortices and their quantised circulation; critical velocities. (Vortex lattice.)
  • Quantum fluctuations and excitations: Feynman arguments about the role of statistics and rotons; number-phase operators and Bogoliubov; nature of the ground state-correlation holes and Jastrow. Order parameters and fluctuations in 1d. The simplest Josephson junction. The strong coupling limit: Bose Hubbard model and the superfluid-insulator transition.
  • Orthogonality catastrophes in the presence of external potentials. Influence of long-range interactions. (Spin-boson models and quantum friction.)
  • Bosons from fermions: are Cooper pairs bosons? plasmons via Bohm-Pines; (Luttinger/Tomonaga).
  • Bosons from spins: hard core bosons as spin 1/2's and half filling; vice-versa, Holstein-Primakoff, Villain; Schwinger.