Anderson's considerations on the flow of superfluid helium: some offshoots

Abstract

Nearly five decades have elapsed since the seminal 1966 paper of P.W. Anderson on the flow of superfluid helium, $^4$He at that time. Some of his "Considerations" -- the role of the quantum phase as a dynamical variable, the interplay between the motion of quantised vortices and potential superflow, its incidence on dissipation in the superfluid and the appearance of critical velocities, the quest for the hydrodynamic analogues of the Josephson effects in helium -- and the way they have evolved over the past half-century are recounted below. But it is due to key advances on the experimental front that phase slippage could be harnessed in the laboratory, leading to a deeper understanding of superflow, vortex nucleation, the various intrinsic and extrinsic dissipation mechanisms in superfluids, macroscopic quantum effects and the superfluid analogue of both {\it ac} and {\it dc} Josephson effects -- pivotal concepts in superfluid physics -- have been performed. Some of the experiments that have shed light on the more intimate effect of quantum mechanics on the hydrodynamics of the dense heliums are surveyed, including the nucleation of quantised vortices both by Arrhenius processes and by macroscopic quantum tunnelling, the setting up of vortex mills, and superfluid interferometry.