Superfluidity

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Discussion

Pyotr Kapitsa, Soviet Union
Helium I vs. helium II. Helium II is a different phase than helium I
Helium liquefies under normal pressures at 4.2 K. From 4.2 K to 2.17 K it behaves like many other liquids, although it has an exceptionally low surface tension and is extremely transparent. Below 2.2 K it behaves quite differently.

• expands upon cooling
• will not boil
• will leak through even the finest pores
• will crawl up and out of its container
• has no viscosity
• is less dense than helium I (which is pretty low as it is)
• has a larger heat of vaporization than helium I (3 million times larger)
• has a lower surface tension than helium I (which is also quite low)
• has no entropy [this must be a misprint]

The mechanisms for this phase transition, and the details of the superfluidity in ⁴He and ³He, are very different. ⁴He has an even number of constituent particles (protons, electrons, and neutrons), which makes it a boson, meaning it is governed by Bose-Einstein statistics. At low temperatures, all the bosons in a sample will want to occupy the same quantum-mechanical ground state, forming a Bose-Einstein condensate. This condensate is responsible for the superfluid behavior of ⁴He below T_λ = 2.17 K.

In contrast, ³He is a fermion, since it has one less neutron than ⁴He. Fermions obey the Pauli exclusion principle, which says that in a sample of many identical fermions, no two can occupy the same quantum-mechanical state. Bose-Einstein condensation is ruled out for ³He, so another mechanism is needed to explain its superfluid behavior. That mechanism is provided by the Bardeen-Cooper-Schrieffer (BCS) theory.

Summary

• bullet

Problems

practice

1. Write something.
   • Answer it.
2. Write something.
   • Answer it.
3. Write something.
   • Answer it.
4. Write something completely different.
   • Answer it.

numerical

1. problems

Resources

• historical
  • Tisza, Laszlo. The λ-Transition Explained. Nature 141 (1938): 643-644 & 913.
  • Allen, J.F. & H. Jones. The Fountain Effect. Nature 141 (1938): 243-244.
  • Kapitza, Pyotr. Superfluidity Observed. Nature 141 (1938): 74 & 75.

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