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A new theory for systems against Newton’s third law


The flocks of birds can also be thought of as breaking symmetry: Instead of flying in random directions, they align like gyros in a magnet. But there is an important difference: The ferromagnetic phase transition can be easily explained using statistical mechanics because it is a system in equilibrium.

But birds — and the cells, bacteria and cars in traffic — add new energy to the system. “Because they have an inner energy source, they behave differently,” says Reichhardt. “And because they don’t conserve energy, it comes out of nowhere, as far as the system is concerned.”

Going beyond quantum

Hanai and Littlewood began their investigation of BEC phase transitions by thinking about well-known, conventional phase transitions. Consider water: Although liquid water and steam look different, Littlewood says, there’s essentially no symmetrical distinction between them. Mathematically, at the time of transition, the two states cannot be distinguished. In a system at equilibrium, that point is called the critical point.

Important phenomena appear everywhere — in cosmology, high-energy physics, even biological systems. But in all of these examples, the researchers could not find a good model for the condensates that form when quantum mechanical systems combine with the environment, undergoing constant damping and pumping. customary.

Hanai and Littlewood suspect that critical points and special points must share some important properties, even if they clearly arise from different mechanisms. “The tipping points are an interesting form of mathematical abstraction, where you cannot tell the difference between the two periods,” Littlewood says. Exactly the same thing happens in these polariton systems.”

They also know that under the guise of mathematics, a laser – technically a state of matter – and a polarized excited BEC have the same fundamental equation. In a piece of paper Published in 2019, researchers connected the dots, proposing a new and important universal mechanism by which peculiar points give rise to phase transitions in quantum dynamical systems.

“We believe that is the first explanation for those conversions,” says Hanai.

Vitelli and Michel Fruchart, also of the University of Chicago, joined Littlewood and Hanai in extending their quantum work to all non-atomic systems, using the mathematical framework of dichotomy and letter theory. relax common assumptions about the energy landscape.Photo: Kristen Norman / Getty Images

At the same time, says Hanai, they realized that although they were studying a quantum state of matter, their equations did not depend on quantum mechanics. Does the phenomenon they are studying apply to larger and more general phenomena? “We began to suspect that this idea [connecting a phase transition to an exceptional point] can also be applied to classical systems. “

But to pursue that idea, they need help. They approached Vitelli and Michel Fruchart, a postdoctoral researcher in Vitelli’s laboratory who studies unusual symmetries in the classical field. Their work extends to metamaterials, which are rich in unconnected interactions; for example, they may show different responses when pressed to one side or the other and may also display distinctive features.

Vitelli and Fruchart were immediately intrigued. Is there some universal principle at play in polarized condensate, some fundamental law about systems where energy is not conserved?

Start syncing

Now as a quartet, researchers began to search for the general principles underlying the link between irregularity and phase transitions. For Vitelli, that meant thinking with his hands. He was in the habit of building physical-mechanical systems to illustrate difficult, abstract phenomena. For example, in the past he has used Legos to build networks that become topological materials that move on edges other than the inside.

“Even though what we’re talking about is theory, you can prove it with toys,” he said.

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