Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Study offers new theoretical approach to describing non-equilibrium phase transitions

27.04.2017

Imaginary numbers are a solution to a very real problem in a study published today in Scientific Reports.

Two physicists at the U.S. Department of Energy's Argonne National Laboratory offered a way to mathematically describe a particular physics phenomenon called a phase transition in a system out of equilibrium.


Two Argonne physicists offered a way to mathematically describe a particular physics phenomenon called a phase transition in a system out of equilibrium (that is, with energy moving through it) by using imaginary numbers. The illustration relates the phase transition to the change between mathematical Mobius transformations (a, b, and c). The theory of out-of-equilibrium physics is a long-sought goal in the field, and could eventually help us design better electronics.

Credit: Vinokur/Galda/Argonne National Laboratory

Such phenomena are central in physics, and understanding how they occur has been a long-held and vexing goal; their behavior and related effects are key to unlocking possibilities for new electronics and other next-generation technologies.

In physics, "equilibrium" refers to a state when an object is not in motion and has no energy flowing through it. As you might expect, most of our lives take place outside this state: we are constantly moving and causing other things to move.

"A rainstorm, this rotating fan, these systems are all out of equilibrium," said study co-author of the Valerii Vinokur, an Argonne Distinguished Fellow and member of the joint Argonne-University of Chicago Computation Institute.

"When a system is in equilibrium, we know that it is always at its lowest possible energy configuration, but for non-equilibrium this fundamental principle does not work; and our ability to describe the physics of such systems is very limited."

He and co-author Alexey Galda, a scientist with Argonne and the University of Chicago's James Franck Institute, had been working on ways to describe these systems, particularly those undergoing a phase transition - such as the moment during a thunderstorm when the charge difference between cloud and ground tips too high, and a lightning strike occurs.

They found their new approach to non-equilibrium physics in a new branch of quantum mechanics. In the language of quantum mechanics, the energy of a system is represented by what is called a Hamiltonian operator. Traditionally, quantum mechanics had held that the operator to represent the system cannot contain imaginary numbers if it would mean the energy does not come out as a "real" and positive value--because the system actually does exist in reality. This condition is called Hermiticity.

But physicists have been taking a harder look at operators that violate Hermiticity by using imaginary components, Vinokur said; several such operators discovered a few years ago are now widely used in quantum optics.

"We noticed that such operators are a beautiful mathematical tool to describe out-of-equilibrium processes," he said.

To describe the phase transition, Galda and Vinokur wrote out the Hamiltonian operator, introduced an applied force to take it out of equilibrium, and then they made the force imaginary.

"This is a trick which is illegal from any common-sense point of view; but we saw that this combination, energy plus imaginary force, perfectly mathematically describes the dynamics of the system with friction," Vinokur said.

They applied the trick to describe other out-of-equilibrium phase transitions, such as a dynamic Mott transition and a spin system, and saw the results agreed with either observed experiments or simulations.

In their latest work, they connected their description with an operation called a Möbius transformation, which appears in a branch of mathematics called topology. "We can understand non-equilibrium transitions now as topological transitions in the space of energy," Galda said.

This bit of quantum mischief needs to be understood more deeply, they said, but is valuable all the same; the theory describes basic areas of physics that are of great interest for next-generation electronics technology.

"For the moment the connection with topology looks like mathematical candy, a beautiful thing we can't yet use, but we know from history that if the math is elegant enough, very soon its practical implications follow," Vinokur said.

###

The study, "Linear dynamics of classical spin as Möbius transformation," was funded by the U.S. Department of Energy's Office of Science, Office of Basic Energy Sciences (Materials Science and Engineering Division).

Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation's first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America's scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy's Office of Science.

The U.S. Department of Energy's Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the Office of Science website.

Media Contact

Jared Sagoff
jsagoff@anl.gov
630-252-5549

 @argonne

http://www.anl.gov 

Jared Sagoff | EurekAlert!

More articles from Physics and Astronomy:

nachricht Quantum optics allows us to abandon expensive lasers in spectroscopy
22.11.2017 | Lomonosov Moscow State University

nachricht Nano-watch has steady hands
22.11.2017 | University of Vienna

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Nanoparticles help with malaria diagnosis – new rapid test in development

The WHO reports an estimated 429,000 malaria deaths each year. The disease mostly affects tropical and subtropical regions and in particular the African continent. The Fraunhofer Institute for Silicate Research ISC teamed up with the Fraunhofer Institute for Molecular Biology and Applied Ecology IME and the Institute of Tropical Medicine at the University of Tübingen for a new test method to detect malaria parasites in blood. The idea of the research project “NanoFRET” is to develop a highly sensitive and reliable rapid diagnostic test so that patient treatment can begin as early as possible.

Malaria is caused by parasites transmitted by mosquito bite. The most dangerous form of malaria is malaria tropica. Left untreated, it is fatal in most cases....

Im Focus: A “cosmic snake” reveals the structure of remote galaxies

The formation of stars in distant galaxies is still largely unexplored. For the first time, astron-omers at the University of Geneva have now been able to closely observe a star system six billion light-years away. In doing so, they are confirming earlier simulations made by the University of Zurich. One special effect is made possible by the multiple reflections of images that run through the cosmos like a snake.

Today, astronomers have a pretty accurate idea of how stars were formed in the recent cosmic past. But do these laws also apply to older galaxies? For around a...

Im Focus: Visual intelligence is not the same as IQ

Just because someone is smart and well-motivated doesn't mean he or she can learn the visual skills needed to excel at tasks like matching fingerprints, interpreting medical X-rays, keeping track of aircraft on radar displays or forensic face matching.

That is the implication of a new study which shows for the first time that there is a broad range of differences in people's visual ability and that these...

Im Focus: Novel Nano-CT device creates high-resolution 3D-X-rays of tiny velvet worm legs

Computer Tomography (CT) is a standard procedure in hospitals, but so far, the technology has not been suitable for imaging extremely small objects. In PNAS, a team from the Technical University of Munich (TUM) describes a Nano-CT device that creates three-dimensional x-ray images at resolutions up to 100 nanometers. The first test application: Together with colleagues from the University of Kassel and Helmholtz-Zentrum Geesthacht the researchers analyzed the locomotory system of a velvet worm.

During a CT analysis, the object under investigation is x-rayed and a detector measures the respective amount of radiation absorbed from various angles....

Im Focus: Researchers Develop Data Bus for Quantum Computer

The quantum world is fragile; error correction codes are needed to protect the information stored in a quantum object from the deteriorating effects of noise. Quantum physicists in Innsbruck have developed a protocol to pass quantum information between differently encoded building blocks of a future quantum computer, such as processors and memories. Scientists may use this protocol in the future to build a data bus for quantum computers. The researchers have published their work in the journal Nature Communications.

Future quantum computers will be able to solve problems where conventional computers fail today. We are still far away from any large-scale implementation,...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Ecology Across Borders: International conference brings together 1,500 ecologists

15.11.2017 | Event News

Road into laboratory: Users discuss biaxial fatigue-testing for car and truck wheel

15.11.2017 | Event News

#Berlin5GWeek: The right network for Industry 4.0

30.10.2017 | Event News

 
Latest News

Corporate coworking as a driver of innovation

22.11.2017 | Business and Finance

PPPL scientists deliver new high-resolution diagnostic to national laser facility

22.11.2017 | Physics and Astronomy

Quantum optics allows us to abandon expensive lasers in spectroscopy

22.11.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>