Nonclassical rotational behavior at the vicinity of the λ point

The rotational property of a quantum liquid at the vicinity of the lambda point T-lambda is examined. In a liquid helium 4 just above T-lambda, 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 of a different nature from the thermal fluctuations. It must affect the rotational properties, such as the moment of inertia. Beginning with the bosons without the condensate, we make a perturbation calculation of its susceptibility with respect to the repulsive interaction, and examine how, with decreasing temperature, the growth of the coherent wave function gradually changes the rotational behavior of a liquid: The moment of inertia slightly decreases just above T-lambda. This means that at the vicinity of T-lambda, the mechanical superfluid density does not always agree with the thermodynamical one. We compare the result to the experiment by Hess and Fairbank [Phys. Rev. Lett. 19, 216 (1967)]. An interpretation of the shear viscosity just above T-lambda is given from this viewpoint.