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Recent work on testing SuperSolidity on Solid Helium 4 has focused on the supposedly lack of intensive property (temperature) dependence of the Helium 4 SuperSolidity.
Well, this is exactly what I would expect. The supersolidity should comes as a function of the temperature, which makes the wavefunction be more extended. It should also be a function of the geometry, that is, the Supersolid Helium 4 only happens around the axis of rotation. The extent (radius of SuperSolidity) is defined by the temperature.
This is not supposed to be a phenomena that is only dependent upon temperature.
The rotation is what makes a Solid a SuperSolid. A solid object rotating has a mirror reflection symmetry with respect to tangential velocities (antisymmetric with respect to R). This means that as the wavefunction of individual Helium 4 atoms spreads, they will overlap with positions radially opposed. The expected momentum is zero for such Bose Condensate, so its contribution to the moment of inertia, disappears.
Of course, if you can only see Three Spatial Dimensions, you will have a very hard time understanding this.
Cheers,
MP
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