By Published: Sept. 9, 2021

Understanding viscosity of strongly bonded particles may hold the key for quantum computing, clean energy

Substances have varying viscosities—honey drips slowly off a dipper, while wine pours freely and easily from the bottle—and those different thicknesses or stickiness can tell them a lot about a specific material or substance’s physical properties.

New research from the University of Colorado Boulder, recently published in Physical Review Letters, shows that it’s possible to calculate the viscosity of a substance with very strongly bonded particles, a phenomenon known as infinite coupling. The calculation, which was previously thought to be impossible, is an important first step toward understanding substances with promising potential for everything from quantum computing to clean energy.

Paul Romatschke

Paul Romatschke, above, is CU Boulder associate professor of physics and the study’s author.

"This paper basically says, 'Just shut up and calculate,'" said Paul Romatschke, CU Boulder associate professor of physics and the study’s author. "You basically just barrel through. Normally, this is an impossible calculation to do for most substances. However, if you cleverly select the substance you’re calculating, there is a way to do it. This is the first time there is a calculation of a viscosity value for a substance at infinite coupling without any conjectures, without any hand-waving."

Scientists have yet to discover a definitive upper limit for viscosity—they keep finding substances with increasingly larger and larger viscosity values, or substances with very high resistance when flowing around an obstacle. (For example, it takes between seven and 13 years for a single drop of pitch tar to fall because of the substance’s extremely high viscosity.)

There does seem to be a lower limit for viscosity, however. Substances like superfluid helium and ultra-cold quantum gasses have extremely low viscosity values around 0.1 to 0.2.

Scientists have also determined that materials with low viscosity values tend to have very strongly coupled particles, which has led them to wonder about the viscosities of substances with infinite coupling.

"Experimentally, you can’t do that—there’s a limit to how much you can crank up the coupling—but theoretically you can," Romatschke said.

Calculating viscosity at weak coupling is difficult to begin with, and it’s generally considered to be impossible at infinite coupling. To get around this hurdle, physicists typically use a conjecture first developed in the 1990s. However, the conjecture is unproven, so researchers would ideally like to be able to perform this calculation without it. That’s where Romatschke’s latest work comes into play.

"This calculation can be done, it doesn’t involve any conjecture and you get a good result," he said. "It opens a window to allow you to do calculations where people normally shook their heads and said, 'That’s completely impossible, nobody can do that.' It is essentially showing a road map on how to progress in the future. We can look at other problems in physics and hopefully understand more about these exciting substances that are strongly coupled."

Some of the substances that scientists would like to better understand include graphene, a two-dimensional sheet of engineered graphite with properties that could prove useful in the realm of quantum computing.

This calculation is essentially showing a road map on how to progress in the future."

Others are high-temperature superconductors, or materials that could conduct electricity at room temperature without any losses. Using Romatschke’s calculation, researchers may be able to better predict which substances would make good high-temperature superconductors.

"Basically, it’s one of the holy grails of clean energy, because if you have a high-temperature superconductor, you can store current infinitely as if it’s a giant battery and never lose any efficiency," he said. "You could store a lot of energy in it and drain it out as you want to. It would revolutionize energy storage in real-world applications."

The calculation also has the potential to help researchers check and verify the accuracy of their quantum computing and machine learning systems, Romatschke said.

"This is something that no classical computer can do, but potentially a quantum computer could calculate something like this and then you would want to know whether it has the right answer," he said. "You can validate the quantum computer by calculating this same property and comparing it with the values in the paper."