# QM and helium superfluid

## Main Question or Discussion Point

So I was checking out some cool videos on youtube of helium in superfluid state and I have a question about it.

How exactly does this superfluid have both zero and non-zero viscosity at the same time?

The evidence seems pretty clear that it exhibits zero viscosity since it forms a Rollin film and it can appear non-zero because if you spin a drum inside it the fluid begins to turn. It is also known that it is not a mix of two types of fluid but rather one fluid that exhibits both properties at the same time (100% of the fluid will drain through a Rollin film not just a zero viscosity portion of it). So how is this possible? Does it have anything to do with QM? Is it like a macroscopic superposition of both zero and non-zero viscosity fluid?

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Hello,

a simple model of superfluid helium is the two-liquid-model and as you said it is surely just an approximation. But you can explain these observations with this model.
If you investigate the rotation of liquid helium while cooling it below the $$\lambda$$-point (phase transition from normal-fluid to superfluid), one would expect a change in the surface of the fluid, because the superfluid part should stop rotating. Although this does not happen you can still talk about non-viscosity of the superfluid part.

If one assumes no turbulences, i.e. no viscosity, it can be shown with stokes that in a simply connected area there can be no rotation of the suprafluid, but another phenomenon of suprafluidity is the formation of vortices. These vortices devide the former simply connected surface in a "ring-shaped" area, where rotation unequal zero is allowed - even for a non-viscosity fluid.

if you spin a drum inside it the fluid begins to turn
This observation per se is no contradiction to the non-viscosity of the superfluid part of superfluid helium. One can argue that only the normal-fluid part is spinning.

SpectraCat
So I was checking out some cool videos on youtube of helium in superfluid state and I have a question about it.

How exactly does this superfluid have both zero and non-zero viscosity at the same time?

The evidence seems pretty clear that it exhibits zero viscosity since it forms a Rollin film and it can appear non-zero because if you spin a drum inside it the fluid begins to turn. It is also known that it is not a mix of two types of fluid but rather one fluid that exhibits both properties at the same time (100% of the fluid will drain through a Rollin film not just a zero viscosity portion of it). So how is this possible? Does it have anything to do with QM? Is it like a macroscopic superposition of both zero and non-zero viscosity fluid?
Liquid helium can be explained using a two fluid model, originally figured out by Lev Landau, and independently by Tisza. Below the lambda point, liquid helium consists of coexisting normal fluid phase and superfluid phases; the superfluid fraction increases as the temperature increases. The superfluid phase flows with zero viscosity (below a critical velocity), and is responsible for the cool phenomena that have you so interested (me too!).

The two fluid model was experimentally verified by Andronikashvili, in an ingenious experiment that used a stack of rotating disks to measure the inertial coupling of the fluid as a function of temperature. This both verified the two-fluid model, and measured the critical velocity.

The superfluidity was explained by Feynman, and yes, it is due to quantum mechanics. The full explanation can be found in his Statistical Mechanics book (Ch. 12 I think). The short version is that the superfluid fraction comes into existence when the de Broglie wavelength of the He atoms reaches the length scale of the average internuclear distance in the fluid. Quantum nuclear symmetry also enters into it, because 4-helium atoms are bosons, and the overall system must be invariant to exchange of identical nuclei. So basically it is very hard to create the sort of low-energy, local excitations that typically characterize dissipative interactions in normal liquids. (I know this is probably unsatisfying, but I have to run to a meeting .. I'll try to post more later).