The 3He and 4He isotopes of helium are quantum fluids at a few K. Helium three, which is well described by the Fermi gas model, has a linear specific heat, and it returns from the solid to the liquid state when it is cooled at suitably chosen pressures. Helium four, which can roughly be described by the Bose gas model, has a phase transition leading from the normal liquid to a new low-temperature liquid phase, called helium II, where a macroscopic fraction of the atoms are condensed into the zero-momentum state. Its specific heat is infinite at the critical point. Helium II is superfluid, and has macroscopic quantum properties, similar to those of superconducting materials.
KeywordsLiquid Helium Grand Canonical Ensemble Bose Condensation Fermi Temperature Average Occupation Number
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