Physicists hit on mathematical description of superfluid dynamics

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A 2001 photo from the space shuttle shows a phenomenon called von Karman vortices in clouds downwind from Rashiri Island in the northern Sea of Japan. The vortices are similar to those that form in superfluids. (NASA)

(PhysOrg.com) -- It has been 100 years since the discovery of superconductivity, a state achieved when mercury was cooled, with the help of liquid helium, to nearly the coldest temperature achievable to form a superfluid that provides no resistance to electrons as they flow through it.

During that century, scientists have struggled to find a precise mathematical explanation of why and how this strange fluid behaves as it does. Liquid helium-4 itself becomes a superfluid when cooled to within a few degrees of absolute zero on the Kelvin scale (minus 273 Celsius or minus 460 Fahrenheit), and the resulting lack of viscosity allows it to seem to defy gravity, flowing up and over the sides of a container.

Now a team led by a University of Washington physicist, using the most powerful supercomputer available for open science, has devised a theoretical framework that explains the real-time behavior of superfluids that are made of fermions ? subatomic particles such as electrons, protons and neutrons that are basic building blocks of nature.

Such superfluids are found in neutron stars, which rotate between one and 1,000 times a second. These stars, also called pulsars, have 50 percent greater mass than the sun but are packed so densely that one can occupy an area only about the size of a city such as Seattle, said Aurel Bulgac, a UW physics professor and lead author of a paper in the June 10 edition of Science that details the work.

As a neutron star rotates, the superfluid on the surface behaves quite differently than a liquid would on the surface of the Earth. As the rotational speed increases the fluid opens a series of small vortices. As the vortices assemble into triangular patterns, the triangles build a lattice structure within the superfluid.

"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."

Similar behavior can be recreated in a laboratory using a vacuum chamber and a laser beam to create a high-intensity electrical field that will cool a small sample, perhaps 1 million atoms, to temperatures near absolute zero. A "laser spoon" then can stir the superfluid fast enough to create vortices.

In trying to understand the odd behavior, scientists have attempted to devise descriptive equations, as they might 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.

The challenge, Bulgac said, was to formulate the proper mathematical problem and then find a computer that could work through the problem as the number of variable changes reached 1 trillion or more. To reach its solution, the team in the last year 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).

"This tells you the complexity of these calculations and how difficult this is," he said.

The researchers also found through their calculations that by increasing the speed at which the fluid was stirred, eventually it would lose its superfluid properties ? though not as soon as had been previously hypothesized. Video representations of the results of the massive numerical simulations are at http://www.phys.washington.edu/groups/qmbnt/UFG.

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.

"This is a pretty major step forward in studying these dynamic processes," he said.

Provided by University of Washington (news : web)

Researchers record two-state dynamics in glassy silicon

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University of Illinois chemistry professor Martin Gruebele led a group that directly observed two-state dynamics in glassy silicon for the first time. Credit: L. Brian Stauffer

Using high-resolution imaging technology, University of Illinois researchers have answered a question that had confounded semiconductor researchers: Is amorphous silicon a glass? The answer? Yes ? until hydrogen is added.

Led by chemistry professor Martin Gruebele, the group published its results in the journal Physical Review Letters.

Amorphous silicon (a-Si) is a semiconductor popular for many device applications because it is inexpensive and can be created in a flexible thin film, unlike the rigid, brittle crystalline form of silicon. But the material has its own unusual qualities: It seems to have some characteristics of glass, but cannot be made the way other glasses are.

Most glasses are made by rapidly cooling a melted material so that it hardens in a random structure. But cooling liquid silicon simply results in an orderly crystal structure. Several methods exist for producing a-Si from crystalline silicon, including bombarding a crystal surface so that atoms fly off and deposit on another surface in a random position.

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A time-lapse video of an amorphous silicon surface. The lumps are clusters of about five atoms of silicon. The "hopping" motion of the lumps shows that a-Si is a glass. Credit: Martin Gruebele

To settle the debate on the nature of a-Si, Gruebele's group, collaborating with electrical and computer engineering professor Joseph Lyding's group at the Beckman Institute for Advanced Science and Technology, used a scanning tunneling microscope to take sub nanometer-resolution images of a-Si surfaces, stringing them together to make a time-lapse video.

The video shows a lumpy, irregular surface; each lump is a cluster about five silicon atoms in diameter. Suddenly, between frames, one bump seems to jump to an adjoining space. Soon, another lump nearby shifts neatly to the right. Although few of the clusters move, the action is obvious.

Such cluster "hopping" between two positions is known as two-state dynamics, a signature property of glass. In a glass, the atoms or molecules are randomly positioned or oriented, much the way they are in a liquid or gas. But while atoms have much more freedom of motion to diffuse through a liquid or gas, in a glass the molecules or atom clusters are stuck most of the time in the solid. Instead, a cluster usually has only two adjoining places that it can ferry between.

"This is the first time that this type of two-state hopping has been imaged in a-Si," Gruebele said. "It's been predicted by theory and people have inferred it indirectly from other measurements, but this is the first time we're been able to visualize it."

The group's observations of two-state dynamics show that pure a-Si is indeed a glass, in spite of its unorthodox manufacturing method. However, a-Si is rarely used in its pure form; hydrogen is added to make it more stable and improve performance.

Researchers have long assumed that hydrogenation has little to no effect on the random structure of a-Si, but the group's observations show that this assumption is not quite correct. In fact, adding hydrogen robs a-Si of its two-state dynamics and its categorization as a glass. Furthermore, the surface is riddled with signs of crystallization: larger clusters, cracks and highly structured patches.

Such micro-crystalline structure has great implications for the properties of a-Si and how they are studied and applied. Since most research has been conducted on hydrogenated a-Si, Gruebele sees a great opportunity to delve into the largely unknown characteristics of the glassy state.

"In some ways, I think we actually know less about the properties of glassy silicon than we think we do, because a lot of what's been investigated of what people call amorphous or glassy silicon isn't really completely amorphous," Gruebele said. "We really need to revisit what the properties of a-Si are. There could yet be surprises in the way it functions and the kind of things that we might be able to do with it."

Next, the group hopes to conduct temperature-depended studies to further establish the activation barriers, or the energy "humps" that the clusters must overcome to move between positions.

More information: Direct Imaging of Two-State Dynamics on the Amorphous Silicon Surface, Phys. Rev. Lett. 106, 235501 (2011) DOI:10.1103/PhysRevLett.106.235501

Abstract

Amorphous silicon is an important material, amidst a debate whether or not it is a glass. We produce amorphous Si surfaces by ion bombardment and vapor growth, and image discrete Si clusters which hop by two-state dynamics at 295 K. Independent of surface preparation, these clusters have an average diameter of ~5 atoms. Given prior results for metallic glasses, we suggest that this cluster size is a universal feature. The hopping activation free energy of 0.93±0.15??eV is rather small, in agreement with a previously untested surface glass model. Hydrogenation quenches the two-state dynamics, apparently by increasing surface crystallinity.

Provided by University of Illinois at Urbana-Champaign (news : web)