ABSTRACT
The difference between normal systems and superfinid systems is perhaps most strikingly manifested in their current flow. Superfluid current flow displays very special features, both in its structure and in its response to external probes. We now focus our attention on these characteristic “superfluid” properties at zero-temperature. The generalization of the theory to finite temperatures is postponed until Chapter 6. Two fundamental features of superfluid flow are the following:
Superfluid flow is irrotational This property may be viewed in a number of ways. In the language of a two-fluid model, it is expressed by the equation: ∇ × v s = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429495717/2cc6e3e4-f702-48c8-b407-59783ef3d6a6/content/eq89_v2.tif"/>
where v s is the superfluid velocity, which we shall define more precisely in Chapter 5. More conveniently, we may say that it is impossible to set up rotational currents on a macroscopic scale in a superfluid. It follows that when a transverse probe is applied to the fluid, the latter does not respond. For example, let us imagine a simple experiment, in which a bucket of helium is rotated at a constant angular velocity ω. In a frame of reference which rotates along with the walls, the fluid feels a Coriolis force, which acts as a transverse probe applied to the system. A normal liquid would respond to such a probe; at equilibrium, the liquid would be dragged by the walls and rotate at the same angular velocity ω. In a homogeneous superfluid at T = 0, the liquid does not respond to the 50Coriolis force; it stays at rest while the walls are rotating. In an actual superfluid, we shall see that matters are more complicated, in that vortices may appear in the rotating bucket. As a result, one does not encounter the dramatic manifestation of superfluid behavior predicted for a homogeneous superfluid. Nevertheless, the above fictitious experiment is conceptually very important, as it illustrates an essential feature of superfluids, namely their rigidity against transverse probes. The physical importance of such a concept is even more obvious in superconductors, since in that case it corresponds to the Meissner effect.
Superfluid flow is resistance free: when a superfluid flows in a thin capillary, it is not slowed down by the walls. The flow thus persists without any pressure head applied to the end of the capillary.
