Using computer modeling, scientists at the University of Cambridge studied new phases of matter called prethermal discrete time crystals (DTCs).
DTCs are highly complex physical systems. They break a distinct time-translational symmetry because, when ‘shaken’ periodically, their structure changes at every ‘push.’
Predicted initially in 2012, the DTCs are being studied in several experiments. Thye are relatively simple-to-realize systems that don’t heat quickly as would usually be expected but instead exhibit time-crystalline behavior for a very long time: the quicker they are shaken, the longer they survive.
The properties of preterminal DTCs were thought to rely on quantum physics. But this new study used a simpler approach based on classical physics to understand this mysterious phenomenon.
Andrea Pizzi, a Ph.D. candidate in Cambridge‘s Cavendish Laboratory, first author on both papers, said, “This was what we thought was the case with prethermal DTCs. We thought they were fundamentally quantum phenomena, but it turns out a simpler classical approach let us learn more about them.”
“You can think of it like a parent pushing a child on a swing on a playground. Normally, the parent pushes the child, the child will swing back, and then pushes them again. In physics, this is a rather simple system. But if multiple swings were on that same playground and children were holding hands with one another, the system would become much more complex, and far more interesting and less obvious behaviors could emerge. A thermal DTC is one such behavior, in which the atoms, acting sort of like swings, only come back every second or third push, for example.”
The study shows that prethermal DTCs avoid using overly complicated quantum approaches: instead, they use much more affordable classical ones. This way, the scientist can simulate these phenomena in a much more comprehensive way.
In their study, scientists used a computer simulation to study many interacting spins under the action of a periodic magnetic field. For this, they used an approach called classical Hamiltonian dynamics.
The resulting dynamics showed neatly and clearly the properties of prethermal DTCs. For a long time, the magnetization of the system oscillates with a period larger than that of the drive.
Pizzi said, “It’s surprising how clean this method is. Because it allows us to look at larger systems, it makes very clear what’s going on. Unlike when we’re using quantum methods, we don’t have to fight with this system to study it. We hope this research will establish classical Hamiltonian dynamics as a suitable approach to large-scale simulations of complex many-body systems and open new avenues in the study of nonequilibrium phenomena, of which prethermal DTCs are just one example.”
- Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. ‘Classical Prethermal Phases of Matter.’ Physical Review Letters (2021).
- Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle. ‘Classical approaches to prethermal discrete time crystals in one, two, and three dimensions.’ Physical Review B (2021).