A new theory of systems that challenges Newton’s third law


The crowding of birds can also be viewed as a symmetry break: instead of flying in random directions, they are aligned like courses in a magnet. But there is an important difference: the magnetic phase transition can be easily explained using statistical mechanics because it is a system in equilibrium.

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

beyond the sleeve

Hanai and Littlewood began their investigation of BEC phase transitions by thinking about regular and well-known phase transitions. Consider water: Although liquid water and vapor look different, Littlewood says, there is no symmetry difference between them. Mathematically, in phase transition, the two states cannot be distinguished. In a system in equilibrium, this point is called the critical point.

Critical phenomena appear everywhere – in cosmology, high energy physics, and even biological systems. But in all of these examples, the researchers were unable to find a good model of the condensate that forms when quantum mechanics systems are coupled to the environment, and undergo continuous damping and pumping.

Hanai and Littlewood suspected that critical points and exceptional points must share some important characteristics, even if they clearly arise from different mechanisms. “Critical points are a kind of interesting mathematical abstraction, where you can’t distinguish between these two phases. The exact same thing happens in these polariton systems,” Littlewood said.

They also knew that under the mathematical hood, the laser – technically a state of matter – and the Polariton-exciton BEC had the same basic equations. In a paper published in 2019, researchers connect the dots, proposing a crucially new and universal mechanism by which the extraordinary dots lead to phase shifts in quantum dynamical systems.

“We think that was the first explanation for those shifts,” Hannay said.

Vitelli and Michele Frochart, also at the University of Chicago, joined forces with Littlewood and Haney in extending their quantum work to all non-commutative systems, using the mathematical framework of bifurcation theory and relaxing the usual assumptions about the energy landscape.Photo: Kristen Norman/Getty Images

Hanai said they realized around the same time that although they were studying a quantum state of matter, their equations were not based on quantum mechanics. Does the phenomenon they were studying apply to larger and more general phenomena? We’re starting to doubt that idea [connecting a phase transition to an exceptional point] It can be applied to classical systems as well.”

But to chase after that idea, they’ll need help. They approached Vitelli and Michel Fruchart, a postdoctoral researcher in Vitelli’s lab, who studies unusual symmetries in the classical field. Their work extends to metamaterials rich in non-reciprocal interactions; They may, for example, show different reactions when pressed from one side or the other and can also display exceptional points.

Vitelli and Frochart were instantly fascinated. Was there a cosmological principle at play in polariton capacitors, and some basic laws about systems where energy is not conserved?

Get in sync

The researchers, as a group of quartiles, set out to search for general principles that underpin the relationship between non-treatment and phase shifts. For Vitelli, that meant thinking with his hands. He has a habit of constructing mechanical-physical systems to illustrate difficult and abstract phenomena. In the past, for example, Legos were used to build lattices that become topological materials that move differently on the edges than on the inside.

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



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