How is superfluidity in liquid helium explained by quantum mechanics?

In summary, the superfluid helium is a strange and fascinating phenomenon that is due to the effects of quantum mechanics. It has both zero viscosity and non-zero viscosity at the same time, 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. This is possible because of the effects of quantum mechanics, which makes it very hard to create low-energy, local excitations that typically characterize dissipative interactions in normal liquids.
  • #1
superpaul3000
62
1
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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  • #2
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 [tex]\lambda[/tex]-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 divide 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.
 
  • #3
superpaul3000 said:
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).
 

1. What is quantum mechanics and how does it relate to helium superfluid?

Quantum mechanics is a branch of physics that describes the behavior of particles at a microscopic level. It explains how particles, such as helium atoms, behave and interact with each other. Helium superfluidity is a phenomenon that can only be explained by quantum mechanics, as it involves the movement of helium atoms at extremely low temperatures.

2. How is helium superfluid different from regular liquid helium?

Regular liquid helium is a liquid at room temperature, but when it is cooled to near absolute zero (0 Kelvin or -273.15 degrees Celsius), it undergoes a phase transition and becomes a superfluid. This means that it can flow without any resistance or friction, unlike regular liquids which have a viscosity and experience friction when flowing.

3. What are the applications of helium superfluidity?

Helium superfluidity has unique properties that make it useful in various scientific and industrial applications. It is used in cryogenics, as it has the lowest boiling point of any known substance and is essential for cooling materials to extremely low temperatures. It also has applications in medical imaging, such as in MRI machines, and in the study of quantum mechanics.

4. How is helium superfluidity studied and measured?

Scientists use various experimental techniques to study and measure helium superfluidity. One common method is to use a torsional oscillator, which measures the frequency of rotation of a small disk suspended in the superfluid. Another method is to use a vibrating wire resonator, which measures changes in the resonance frequency as the superfluid flows past the wire.

5. Can helium superfluidity exist at room temperature?

No, helium superfluidity can only exist at extremely low temperatures close to absolute zero. This is because the quantum effects that allow for superfluidity become negligible at higher temperatures. However, scientists are researching ways to create superfluidity at higher temperatures by using different materials and techniques.

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