Imaginary numbers present real solution to vexing physics problem

UChicago News

Imaginary numbers are a solution to a very real problem, according to a new study published in Scientific Reports.Two physicists at Argonne National Laboratory offered a way to mathematically describe a particular physics phenomenon called a phase transition in a system out of equilibrium. 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 Computation Institute at the University of Chicago. “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 ...

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