Superfluid Helium

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 HeII is a quiscent


Some unusual properties of HeII:
 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)

 Thermomechanical couplings:
 No boiling bubbles
 Heating of a pressurized compartment in the superflow experiment
 The fountain effect

Is superfluidity related to BoseEinstein 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 thermomechanical
effects.
 Key differences of helium superfluidity and BEC:
 Interactions: HeII is a practically incompressible liquid due
to hardcore interactions, while the ideal BEC has no compressibility!
 Differences in the heatcapacity curves:
 There is a λlike 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)
 In closing:
8.333 Superfluid Helium last update 12/12/16
by M. Kardar