The onset of superfluidity in capillary flow of liquid helium 4
  The onset mechanism of superfluidity is examined by taking the case of the capillary flow of liquid helium 4. In the capillary flow, a substantial fall of the shear viscosity has been observed in the normal phase (lambda point<T<3.7K). In this temperature region, under the strong influence of Bose statistics, the coherent many-body wave function grows to an intermediate size between a macroscopic and a microscopic one, which is different from thermal fluctuation. We consider such a capillary flow by including it to a general picture that includes the flow of rotating helium 4 as well. Using the Kramers-Kronig relation, we express the inverse of the shear viscosity in terms of the generalized susceptibility of the system, and obtain a formula for the shear viscosity in the vicinity of the lambda point. Regarding bosons without the condensate as a non-perturbative state, we make a perturbation calculation of the susceptibility with respect to the repulsive interaction. With decreasing temperature from 3.7K, the growth of the coherent wave function gradually suppresses the shear viscosity, and makes the superfluid flow stable. Comparing formulas obtained to the experimental data, we estimate that the ratio of the superfluid density defined in the mechanical sense reaches 1/100000 just above the lambda point. 
Shun-ichiro Koh