Shear viscosity and Bose statistics: Capillary flow above lambda point

TL;DR

This paper investigates how Bose statistics influence shear viscosity in liquid helium-4 above the lambda point, revealing a precursor to superfluidity characterized by reduced viscosity and the growth of coherent many-body wave functions.

Contribution

It introduces a theoretical framework linking Bose statistics to shear viscosity reduction and describes the onset of superfluidity in dissipative flow through susceptibility analysis.

Findings

Shear viscosity decreases significantly above the lambda point due to Bose statistics.

A formula relating susceptibility to shear viscosity is derived.

Liquid helium-4 exhibits anomalously low viscosity even in the normal phase.

Abstract

The gradual fall of the shear viscosity below 2.8K, observed in a liquid helium 4 flowing through a capillary, is examined. The disappearance of the shear viscosity in a capillary flow is a manifestation of superfluidity in dissipative phenomena, the onset mechanism of which is a subtle problem compared to that of superfluidity in non-dissipative phenomena. Applying the linear-response theory to the reciprocal of the shear viscosity coefficient, we relate these two types of superfluidity using the Kramers-Kronig relation. We obtain a formula describing the influence of Bose statistics on the kinematic shear 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 shear viscosity coefficient. Hence, although in the normal phase, it is already an anomalous liquid 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, not as a thermal fluctuation but as a thermal equilibrium state. Beginning with bosons without the condensate, we make a perturbation calculation of its susceptibility with respect to the repulsive interaction. We examine how, with decreasing temperature, the growth of the coherent wave function gradually suppresses the shear viscosity, and finally leads to a frictionless flow at the lambda-point.