Superfluid Helium

  1. Helium stays fluid down to T=0°K, since
    • The van der Waals attraction between helium atoms is weak (closed electronic shells)
    • Quantum fluctuations are large (light mass)
    • Phase diagram of helium:                       
    • The isotope He4 (but not He3) undergoes a phase transition to a new state at T=2.18°K
    • In evaporative cooling boiling stops, and He-II is a quiscent
  2. Some unusual properties of He-II:
    • The puzzle of its viscosity:
      • It flows through the finest capillaries with no apparent resistance 
      • There is a finite drag of fluid in torsional experiments (Keesom, Andronikashvilli)
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    • Thermo-mechanical couplings:
      • No boiling bubbles
      • Heating of a pressurized compartment in the superflow experiment
      • The fountain effect
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  3. Is superfluidity related to Bose-Einstein Condensation (BEC)? (Fritz London, 1938)
    • It does not occur in the fermionic isotope of He3
    • The predicted BEC transition temperature of  Tc=3.13°K at the density of helium is not far off.
    • Lazlo Tisza's two fluid model can explain the thermo-mechanical effects.
  4. Key differences of helium superfluidity and BEC:
    • Interactions: He-II is a practically incompressible liquid due to hard-core interactions, while the ideal BEC has no compressibility!
    • Differences in the heat-capacity curves:
      • There is a λ-like logarithmic divergence in heat capacity, as opposed to the finite hump in BEC
      • Heat capacity vanishes as T^{3} at low temperatures, as opposed to T^{3/2} for BEC
    • Differences in the superfluid fraction:
      • The superfluid fraction not vanish linearly at the transition point
      • The normal fraction does not vanish as T^{3/2} at zero temperature
    • There can be no superfluidity if the spectrum of excitations scales quadratically in momentum [cf Kelvin waves excited by wind on water]
    • These differences can be accounted for by the Landau spectrum of elementary excitations (phonons+rotons)
  5. In closing:

8.333  Superfluid Helium