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New theory of systems that defy Newton’s third law

The collection of birds can also be seen as a symmetry break: instead of flying in random directions, they line up like the rotations of a magnet. But there is one important difference: the transition of ferromagnetic phases is easily explained using statistical mechanics because it is a system in equilibrium.

But birds — and the cells in traffic, bacteria, and cars — add new energy to the system. “Because they have an internal energy source, they behave differently,” Reichhardt said. “And because they don’t save energy, it appears out of nowhere, in terms of the system.”

Beyond quantum

Hanaik and Littlewood began research on BEC phase transitions by thinking about common and well-known phase transitions. Consider water: although liquid water and vapor appear to be different, Littlewood said, there is basically no distinction of symmetry between them. Mathematically, at the transition point, the two situations cannot be distinguished. In a system in equilibrium, this point is called the critical point.

Critical phenomena appear everywhere: in cosmology, in high-energy physics, and even in biological systems. But in all of these examples, the researchers were unable to find a good model for the condensates that form when quantum mechanical systems are coupled to the environment, subject to constant deceleration and pumping.

Hanaik and Littlewood suspected that critical points and extra points must share some important properties, even if they clearly arose from different mechanisms. “Critical points are an interesting mathematical abstraction,” Littlewood said, “where you can’t tell the difference between these two phases. The same thing happens in these Polariton systems.”

They also knew that a laser under the mathematical hood — technically a state of matter — and a polariton-exiton BEC had the same underlying equations. In a paper Published in 2019, the researchers linked points and, above all, proposed a new mechanism by which exception points create phase transitions in quantum dynamical systems.

“We think that was the first explanation for those transitions,” Hanai said.

Vitelli and Michel Fruchart, also from the University of Chicago, teamed up with Littlewood and Hanai to extend their quantum work to all non-reciprocal systems, using the mathematical framework of bifurcation theory and calming common assumptions about the energy landscape.Photo: Kristen Norman / Getty Images

Approximately at the same time, Hanai said, they realized that although they were studying the quantum state of matter, their equations were not dependent on quantum mechanics. Did the phenomenon being studied apply to even larger and more general phenomena? “We started to suspect that idea [connecting a phase transition to an exceptional point] they could also be applied to classical systems. ‘

But to follow that idea, they would 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 non-reciprocal interactions; for example, clicking on one side or the other can show different reactions and also show extra points.

Vitelli and Fruchart were immediately impressed. Was there a universal principle in condensed polariton, a basic law about systems that do not conserve energy?

Gets in sync

Now as a quartet, researchers began to search for general principles that underlie the link between reciprocity and phase transitions. For Vitelli, that meant thinking with his own hands. He has a habit of constructing physical and mechanical systems to illustrate difficult and abstract phenomena. In the past, for example, Lego has used them to build networks that become topological materials that move differently at the edges than at the interior.

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

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