A new theory for systems that oppose Newton’s third law

The gathering of birds can also be seen as a violation of symmetry: instead of flying in random directions, they align like rotations in a magnet. But there is an important difference: the ferromagnetic phase transition is easily explained with the help of statistical mechanics, because it is a system in equilibrium.

But birds – and cells, bacteria and cars in traffic – add new energy to the system. “Because they have a source of internal energy, they behave differently,” Reichhard said. “And because they don’t save energy, it comes out of nowhere as far as the system is concerned.”

Beyond the quantum

Hanai and Littlewood began their investigation of BEC phase transitions, thinking of ordinary, well-known phase transitions. Think about water: Although liquid water and steam look different, Littlewood said, there is generally no difference in symmetry between them. Mathematically, at the transition point, the two states are indistinguishable. In an equilibrium system, this point is called the critical point.

Critical phenomena appear everywhere – in cosmology, high energy physics, even in biological systems. But in all these examples, the researchers could not find a good model for the condensates that form when quantum mechanical systems are connected to the environment, subject to constant attenuation and pumping.

Hanai and Littlewood suspected that critical points and exceptional points must share some important properties, even if they obviously stem from different mechanisms. “Critical points are something of an interesting mathematical abstraction,” said Littlewood, “where you can’t understand the difference between these two phases. Exactly the same thing happens in these polariton systems. “

They also knew that under the mathematical cover, the laser – the technical state of matter – and the polariton-exciton BEC have the same basic equations. In a publication published in 2019, researchers link the points, proposing a new and, most importantly, universal mechanism through which exceptional points lead to phase transitions in quantum dynamical systems.

“We believe this was the first explanation for these transitions,” Hanai said.

Vitelli and Michelle Fruchart, also from the University of Chicago, joined Littlewood and Hanai in extending their quantum work to all non-reciprocal systems, using the mathematical framework of bifurcation theory and easing common assumptions about the energy landscape.Photo: Kristen Norman / Getty Images

At about the same time, Hanai said, they realized that although they were studying the quantum state of matter, their equations did not depend on quantum mechanics. Did the phenomenon they were studying refer to even larger and more general phenomena? “It simply came to our notice then [connecting a phase transition to an exceptional point] it can also be applied to classical systems. “

But to pursue this idea, they will need help. They turned to Vitelli and Michelle Fruschart, a postdoctoral fellow in Vitelli’s laboratory who study unusual symmetries in the classical field. Their work extends to metamaterials that are rich in non-reciprocal interactions; they can, for example, show different reactions when pressed on one side or the other and can also show exceptional points.

Vitelli and Frushart were immediately intrigued. Was there a universal principle in the polariton condensate, a fundamental law for systems in which energy is not conserved?


Now as a quartet, researchers have begun to look for common principles that support the link between non-reciprocity and phase transitions. For Vitelli, it meant thinking with his hands. He has a habit of building physico-mechanical systems to illustrate difficult, abstract phenomena. In the past, for example, he used Legos to build grids that turn into topological materials that move differently along the edges than inside.

“Although what we are talking about is theoretical, you can demonstrate it with toys,” he said.

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