Dynamics of Superflow by Mesoscopic Condensate

Abstract

The shear viscosity η of a quantum liquid in the vicinity of T λ is examined. In liquid helium 4 above T λ ( T λ < T <3.7 K), under a strong effect of Bose statistics, the coherent many-body wave function grows to an intermediate size between a macroscopic level and a microscopic one. These wave functions are qualitatively different from thermal fluctuation, and manifest themselves in the gradual decrease in shear viscosity above T λ . To formulate this phenomenon, we combine the correlation function with fluid dynamics. Applying the Kramers–Kronig relation to the generalized Poiseuille's formula for capillary flow, we perform a perturbation calculation of the reciprocal 1/η with respect to the particle interaction, and examine how the growth of coherent wave functions gradually decreases shear viscosity. Comparing with the experimentally determined η( T ), \(\hat{\rho}_{\text{s}}(T)/\rho\) of such a mesoscopic condensate is estimated to reach 10 -5 just above T λ . We examine the effect of condensate size on the stability of such a superflow, and touch upon the superflow in porous media.