# Mathematics Explain Dynamics of Superfluid

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At nearly the coldest temperature possible – mercury (with the aid of liquid helium) – forms a state called superconductivity. At the extreme, electrons flow unencumbered through what is known as a superfluid. But the hows and whys of superfluid behavior defied explanation. Until now…

When taken to within a few degrees of absolute zero on the Kelvin scale (minus 273 Celsius or minus 460 Fahrenheit), liquid helium-4 turns into the remarkable superfluid state. It swirls, it curls, and it’s lack of body has been baffling scientists for nearly a century. Now a team led by a University of Washington physicist, using the most powerful supercomputer available for open science, has cooked up a theoretical picture which explains the real-time behavior of superfluid. Just who is the responsible party here? Try subatomic particles called fermions.

Femions are a much a part of the natural equation as electrons, protons and neutrons… just as superfluids are part of neutron stars. Rotating between one and 1,000 times a second, neutron stars – or pulsars – superfluid surface acts much differently than its counterpart here on Earth. As the speed increases, it forms a series of small vortices which group in a triangular pattern… which in turn forms a braid within the superfluid structure. “When you reach the correct speed, you’ll create one vortex in the middle,” Bulgac said. “And as you increase the speed, you will increase the number of vortices. But it always occurs in steps.”

Can science recreate it? Yes. Laboratory models utilizing a vacuum chamber and a laser beam to create a high-intensity electrical field have managed to chill a small sample, perhaps 1 million atoms, to temperatures near absolute zero. Then a “laser spoon” is employed to stir the superfluid fast enough to create vortices.

“In trying to understand the odd behavior, scientists have attempted to devise descriptive equations, such as ones they might use to describe the swirling action in a cup of coffee as it is stirred.” Bulgac said. “But to describe the action in a superfluid made of fermions, a nearly limitless number of equations is needed. Each describes what happens if just one variable – such as velocity, temperature or density – is changed. Because the variables are linked, if one changes others will change as well.”

One of the major challenges in formulating a mathematical hypothesis is the amount of computing power it would take to work through a problem with a number of variable changes that reached 1 trillion or more. So how did they do it? The team used the JaguarPF computer at Oak Ridge National Laboratory in Tennessee, one of the largest supercomputers in the world, for the equivalent of 70 million hours, which would require almost 8,000 years on a single-core personal computer (JaguarPF has nearly a quarter-million cores). Just try to cool that!

“This tells you the complexity of these calculations and how difficult this is,” Bulgac said. To make matters even more complex, the faster the superfluid is stirred causes it to lose its properties – but not as fast as hypothesized. “The work means that researchers can ‘to some extent’ study the properties of a neutron star using computer simulations.” Bulgac said. .”It also opens new directions of research in cold-atom physics.”

And more homework on our part.

Original Story Source: University of Washington.

## 18 Replies to “Mathematics Explain Dynamics of Superfluid”

1. Anonymous says:

Interesting work – I studied low-temp physics for a while. It’s just so damn awesome.

2. Anonymous says:

Super Fluids are part of Neutron stars?… I thought that it had to be really cold for a substance to become superfluid…

1. Jonathan Shock says:

In the phase diagram of matter which interacts via the strong force, neutron stars are very dense, but not that hot.

1. So inside them, temperatures are in the negative hundreds?! WOW, that’s an epiphanic moment for me, realizing that! What a truly awesomely cool bit of information! Why, why, WHY is this so rarely mentioned in pieces on the topic? Well, the many ones crafted for non-scientist enthusiasts to ‘grok’, that I’ve read, watched and listened to anyway…

2. Tim Reilly says:

I’ve always heard they’re still in the few millions of kelvin, which is still very hot compared to ‘everyday’ temperatures here on Earth. Cold for stars, yes, but still hardly cold.

3. No, neutron stars are not icing up. They are still hot. However, it’s the ridiculously high density and gravity that act to “supercool” the surface so that it ACTS as though it is near absolute zero. That’s my understanding anyway.

4. It makes one wonder whether many answers to the basic questions of cosmology will be answered by very complex equations as opposed to the beautiful simplicity of E=mc (sorry, don’t know how to type a raised small two). Anyway, maybe with computer power doing what it does, we’ll realize that everything interacts and depends on each other such that nothing can really be described with such elegant ease. So much of the basics seem to elude us that one wonders where the answers are hidden. (NOT opening the discussion to Holy Hand Grenades or Giant floating Spaghetti Monsters!)

5. It makes one wonder whether many answers to the basic questions of cosmology will be answered by very complex equations as opposed to the beautiful simplicity of E=mc (sorry, don’t know how to type a raised small two). Anyway, maybe with computer power doing what it does, we’ll realize that everything interacts and depends on each other such that nothing can really be described with such elegant ease. So much of the basics seem to elude us that one wonders where the answers are hidden. (NOT opening the discussion to Holy Hand Grenades or Giant floating Spaghetti Monsters!)

6. Anonymous says:

Use the carrot sign with E = mc^2. That equation is a derived result. It does not constitute the theory of relativity, but is a certain result.

LC

7. IVAN3MAN_AT_LARGE says:

Dude, it’s not “carrot”; it’s the caret sign, or chevron.

8. It makes one wonder whether many answers to the basic questions of cosmology will be answered by very complex equations as opposed to the beautiful simplicity of E=mc (sorry, don’t know how to type a raised small two). Anyway, maybe with computer power doing what it does, we’ll realize that everything interacts and depends on each other such that nothing can really be described with such elegant ease. So much of the basics seem to elude us that one wonders where the answers are hidden. (NOT opening the discussion to Holy Hand Grenades or Giant floating Spaghetti Monsters!)

9. Anonymous says:

A stationary neutron star has no internal heat source. It is not generating energy through fusion. A neutron star in the cold of space will after a few million years cool down to temperature of interstellar space at about 20K. That is pretty cold.

LC

10. IVAN3MAN_AT_LARGE says:

Actually, neutron stars cool off very quickly via neutrino emission. In the early stage of a neutron star’s life, neutrinos are produced copiously; therefore, if the neutrinos have energies less than about 10 MeV, they sail right through the neutron star without interacting and thereby acting as a highly efficient heat-sink.

11. No, neutron stars are not icing up. They are still hot. However, it’s the ridiculously high density and gravity that act to “supercool” the surface so that it ACTS as though it is near absolute zero. That’s my understanding anyway.

3. Happy says:

4. Anonymous says:

There is a condensate state with quark-gluon fluids called the color-flavor locked state. This is a state that should exist in the center of neutron stars where pressures are huge. This is analogous to the superfluid or superconductivity state in a solid at low temperatures. This is a state where quarks of a certain type, called a flavor, lock into a single mode with the same color. Color refers to the “charge” involved with quantum chromodynamics, also known as the strong force.

LC

5. “When taken to within a few degrees of absolute zero on the Kelvin scale”. Not normally one to nit-pick, but the fact that “Kelvin” is not measured in “degrees”, though obviously learned people misuse the phrase anyway, bothers me second only to the myriad ways that the term, “Novae” (Nova~plural) is mangled… Oh, and of course, “Nucular”, but that’s per factoring in general populous ignorance, which is entirely other ball of wax… Apologies for my anal rant. ‘^.^, Aside all that, fascinating research! In another life I’m a Nucular Physicalist… lol!

6. Anonymous says:

“Try subatomic particles called fermions. Femions are a much a part of the natural equation as electrons, protons and neutrons…”
Ummm, highly misleading. Fermions are not subatomic particles per se, they are a class of subatomic particles with half-integer spins (usually 1/2) which obey the statistical Fermi-Dirac distribution equation. Electrons, Protons and Neutrons all ARE Fermions. The counterpart are Bosons (which obey the statistical Bose-Einstein distribution equation), with integer spins (0, 1, 2…), these are the carriers of the forces (Photons, Gluons, W/Z Bosons, Gravitons).

Depending on the number of subatomic particles they consist of, atoms can be bosonic ore fermionic. Bosons have the “ability” to all occupy a single quantum state, which makes creating a Bose-einstein condensate out of Bosonic atoms much easier than making one out of Fermionic atoms, which first need to pair up to creat Bosonic “twins”.

Also, theory has it that the innards of neutron stars are superfluidic, the surfaces are actually an iron lattice crust.