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Mechanism of Superfluid Flow

Abstract

THEORIES of superfluidity usually assume the possibility of pure potential flow, provided that the flow velocity is less than some critical value (at which the creation of excitations first becomes possible)1,2. If we consider the flow of helium (at T = 0° K.), for example through a tube or along a Rollin film, it is implied that the boundary layer is slipping over the solid wall. However, the first few layers of helium atoms would not be expected to take part in this motion, as they are firmly bound by the van der Waals' attractions of the wall. The picture therefore has to be revised slightly to one in which there is a velocity discontinuity (that is, a vortex sheet) close to, but not coincident with, the solid wall. But a continuous vortex sheet implies a rather drastic change in the character of the wave function, over a distance of the order of one interatomic distance a, and hence implies a large energy per unit area, of the order of 2/ma4 (where m is the mass of an atom).

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References

  1. Landau, L. D., J. Phys. (U.S.S.R.), 5, 71 (1941); 11, 91 (1947). Feynman, R. P., Phys. Rev., 94, 262 (1954).

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  2. Feynman, R. P., “Low Temperature Physics”, 1, 17 (North Holland Pub. Co., Amsterdam, 1955). Onsager, L., Nuovo cim. (ix), 6, Supp., 249 (1949).

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  3. See, for example, Milne-Thomson, L. M., “Theoretical Hydrodynamics”, 340 (Macmillan, London, 1948).

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  4. Contrast with the conventional interpretations; see, for example, Atkins, K.R., “Liquid Helium”, 90 (Cambridge University Press, 1959).

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KUPER, C. Mechanism of Superfluid Flow. Nature 185, 832–833 (1960). https://doi.org/10.1038/185832a0

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