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The gradual fall of the shear viscosity below 2.8K, observed in a liquidhelium 4 flowing through a capillary, is examined. The disappearance of theshear viscosity in a capillary flow is a manifestation of superfluidity indissipative phenomena, the onset mechanism of which is a subtle problemcompared to that of superfluidity in non-dissipative phenomena. Applying thelinear-response theory to the reciprocal of the shear viscosity coefficient, werelate these two types of superfluidity using the Kramers-Kronig relation. Weobtain a formula describing the influence of Bose statistics on the kinematicshear viscosity in terms of the susceptibility. Compared to an ordinary liquid,a liquid helium 4 above the lambda point has a 1/1000 times smaller shearviscosity coefficient. Hence, although in the normal phase, it is already ananomalous liquid under the strong influence of Bose statistics. The coherentmany-body wave function grows to an intermediate size between a macroscopic anda microscopic one, not as a thermal fluctuation but as a thermal equilibriumstate. Beginning with bosons without the condensate, we make a perturbationcalculation of its susceptibility with respect to the repulsive interaction. Weexamine how, with decreasing temperature, the growth of the coherent wavefunction gradually suppresses the shear viscosity, and finally leads to africtionless flow at the lambda-point.

Shear viscosity and Bose statistics: Capillary flow above lambda point