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In the vicinity of the superfluid transition in liquid 4He, we explore the relation between two apparently unrelated physical quantities—the kinematic viscosity, ν, in the normal state and the quantum of circulation, κ, in the superfluid state. The model developed here leads to the simple relationship ν ≈ κ/6, and links the classical and quantum flow properties of liquid 4He. We critically examine available data relevant to this relation and find that the prediction holds well at the saturated vapor pressure. Additionally, we predict the kinematic viscosity for liquid 4He along the λ-line at negative pressures.


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