A new phase of matter, thought to be understood only using quantum physics, can be studied using much simpler classical methods.
Researchers from the University of Cambridge have used computer modeling to study potential new phases of matter known as discrete pre-stabilized time crystals (DTCs). The properties of previous DTCs of the aether were thought to depend on quantum physics: the strange laws that govern particles at the subatomic level. However, the researchers found that a simpler approach, based on classical physics, could be used to understand these mysterious phenomena.
Understanding these new phases of matter is a step forward toward controlling complex multi-body systems, and it is a long-standing goal with many potential applications, such as simulating complex quantum networks. The results were reported in two joint papers in physical review messages And physical review b.
When we discover something new, whether it’s a planet, an animal, or a disease, we can learn more about it by looking at it closely. The simpler theories are tried first, and if they don’t work, more complex theories or methods are tried.
“This was what we thought was the case with Erthmal’s previous DTCs,” said Andrea Pizzi, Ph.D. Candidate at the Cavendish Laboratory in Cambridge, first author on both papers. “We thought they were basically quantum phenomena, but it turns out it’s a simpler classical approach so let’s learn more about them.”
DTCs are very complex physical systems, and there is still much to learn about their unusual properties. Like how a standard space crystal breaks space-transition symmetry because its structure is not the same everywhere in space, DTCs break distinct transition symmetry because, when they ‘vibrate’ periodically, their structure changes on each ‘push’.
“You can think of it like a parent pushing a kid on a swing on the playground,” Betzy said. “Usually, the parent pushes the child, the child swings, and then the parent pushes him again. In physics, this is a fairly simple system. But if there are several swings on the same playground, and if the children are holding hands, then the system will become more complex, and they can show more interesting and less obvious behaviors. The pre-ether DTC is one such behavior, where the atoms behave like swaying, only ‘going back’ every second or third batch, for example.”
First predicted in 2012, DTCs have opened up a new field of research, and they have been studied in various types, including experiments. Among these systems, the pre-ethermal DTCs are relatively easy to achieve and do not heat up as quickly as would normally be expected, but instead exhibit a time-crystallizing behavior for a very long time: the faster they are shaken, the longer they remain. However, they were thought to rely on quantum phenomena.
“The development of quantum theories is complex, and even when you run it, your simulation capabilities are very limited, because the computational power required is incredibly large,” said Bizzi.
Now, Bizzi and colleagues have found that for pre-proof DTCs, they can avoid using overly complex quantum approaches and instead use more affordable classical methods. In this way, researchers can simulate these phenomena in a more comprehensive way. For example, they can now simulate many elementary components, giving them access to the scenarios most relevant to experiments, such as in two and three dimensions.
Using computer simulations, the researchers studied several interacting spins – such as children on a swing – under the influence of a periodic magnetic field – such as a parent pushing a swing – using classical Hamiltonian dynamics. The resulting dynamics demonstrated in an elegant and clear way the properties of the pre-ether DTCs: for a long time, the system magnets oscillated with a period greater than that of the drive.
“It’s surprising how clean this method is,” Betzy said. “Because it allows us to look at larger systems, it shows what happens. Unlike when we use quantitative methods, we don’t have to fight with this system to study it. We hope that this research establishes the classical Hamiltonian model of dynamics as a suitable approach for large-scale simulations of complex multi-body systems. and open new approaches in studying non-equilibrium phenomena, of which pre-proven DTCs are just one example.”
Betzi’s co-authors on the two papers, who were recently based in Cambridge, are Dr Andreas Nonenkamp, currently at the University of Vienna, and Dr Johannes Knoll, currently at the Technical University of Munich.
Meanwhile, at UC Berkeley, Norman Yao’s group was also using classical methods to study pre-emergent DTCs. Remarkably, the Berkeley and Cambridge teams tackled the same question at the same time. Yao’s group will publish their results soon.
Observation of a discrete time crystal before the ether
Andrea Pizzi, Andreas Nonenkamp, Johannes Knoll. “Preclassic Matter Phases of Ether.” physical review messages (2021). journals.aps.org/prl/accepted/ … 9c67616f3831df7292f1
Andrea Pizzi, Andreas Nonenkamp, Johannes Knoll. “Classical Approaches to Pre-Ether Discrete Time Crystals in One, Two, and Three Dimensions.” physical review b (2021). journals.aps.org/prb/accepted/ … 551910d68564c223487a
Presented by the University of Cambridge
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