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It is possible to study a new phase of matter with much simpler classical methods than quantum physics.
Computer modeling was used by researchers at the University of Cambridge to examine potential new phases of matter, known as prethermal time crystals (DTCs). The properties of the prethermal DTCs depended on quantum physics, the bizarre laws that govern particles at subatomic scale. The researchers discovered that it was possible to understand these strange phenomena using a simpler approach based on classical Physics.
Understanding the new phases of matter is an important step towards controlling complex many-body systems. This goal has been a long-standing one with many potential applications such as simulations of complex quantum networks. Two papers, one in Physical Review Letters, and one in Physical Review B, report the results.
We can learn more about a new discovery, be it a planet, an animal or a disease, by studying it closer. The first attempts at simpler theories are made, and then, if that fails, more complex theories or methods are developed.
Andrea Pizzi, a Ph.D. student at Cambridge's Cavendish Laboratory and first author of both papers, stated that this was what they believed was the case for prethermal DTCs. We thought they were fundamentally quantum phenomena. But, it turned out that a simpler classical approach allowed us to learn more about them.
DTCs are complex physical systems that have many unknown properties. DTCs are like a space crystal breaking space-translationalsymmetry because its structure doesn't match anywhere in space. DTCs also break time-translationalsymmetry because their structure changes when they're'shaken' regularly.
Pizzi said, "You could think of it as a parent pushing their child on a swing in a park." Pizzi said that a parent would push the child and then the child would swing back. The parent then pushes them once more. This is the simplest system in physics. However, if there were multiple swings on the same playground and children were holding hands, then the system could become more complicated and more interesting. Prethermal DTC, which is a behavior similar to swings, is an example of such a behavior. The atoms 'come back' only every second or third push.
DTCs were first predicted in 2012. They have been extensively studied in many types of experiments and in different types of research. Prethermal DTCs, which are simple to realize, don't heat as quickly as one would expect. Instead, they exhibit time-crystalline behavior that lasts a long time. The faster they are shaken the longer they live. It was believed that they depend on quantum phenomena.
Pizzi stated that "Developing quantum theories can be complicated and your simulation capabilities can often be very limited because of the huge computational power required."
Pizzi and co-authors now know that they can use less expensive classical methods to simulate prethermal DTCs instead of using complex quantum approaches. These researchers are able to simulate these phenomena more effectively. They can now simulate more elementary constituents and access the most relevant scenarios for experiments in two- and three-dimensional dimensions.
The researchers used a computer simulation to study many interactions spins, such as the children swinging under the action of a periodic magnet field or the parent pushing the swing. They also studied classical Hamiltonian dynamics. The resultant dynamics revealed in a clear and concise way the properties prethermal DTCs. For a long period, the magnetisation oscillates with a longer period than the drive.
Pizzi said, "It's amazing how clean this method ist." It allows us to see larger systems and it makes it very clear what is going on. We don't have the need to fight this system, unlike when we use quantum methods. This research is expected to establish classical Hamiltonian dynamics in large-scale simulations complex multi-body systems. It will also open up new avenues for the study of nonequilibrium phenomena such as prethermal DTCs.
Pizzi's coauthors on the papers are Dr. Andreas Nunnenkamp (now at the University of Vienna) and Dr. Johannes Knolle (now at the Technical University of Munich).
Norman Yao's group at UC Berkeley has been studying prethermal DTCs using classical methods. Surprisingly, both the Berkeley and Cambridge teams simultaneously tackled the same question. Yao's group will soon publish their results.
Continue reading: Observing a prethermal discrete-time crystal
