Bose-Einstein Condensation & Superfluidity
Below a critical temperature $T_c$, a macroscopic fraction of bosons occupies the single-particle ground state — Bose-Einstein condensation. In interacting systems like liquid $^4$He, this produces superfluidity: frictionless flow, quantized vortices, and the remarkable two-fluid hydrodynamics first described by Tisza and Landau.
The Gross-Pitaevskii equation provides a mean-field description of weakly interacting condensates, while Bogoliubov theory reveals the phonon-like excitation spectrum that underlies the Landau criterion for superfluidity.
Chapters
1. Bose-Einstein Condensation
Bose-Einstein distribution, critical temperature, condensate fraction, ideal vs interacting BEC, and experimental realizations.
2. Superfluid Helium
Lambda transition, He-II properties, Landau criterion for superfluidity, roton minimum, and fountain effect.
3. Two-Fluid Model
Normal and superfluid components, second sound, mutual friction, and thermal counterflow.
4. Gross-Pitaevskii Equation
Mean-field theory of weakly interacting bosons, healing length, Thomas-Fermi limit, and Bogoliubov excitations.
5. Quantized Vortices
Circulation quantization, vortex lines, Abrikosov lattice, vortex dynamics, and rotating superfluids.