Researchers in Japan have developed a new mathematical technique to explore the characteristics of time crystals. The team, led by Kae Nemoto at the National Institute of Informatics in Tokyo, used a combination of graph theory and statistical mechanics to show how the exotic quantum materials evolve over time. Their work opens new routes to practical applications for time crystals, including simulations of complex quantum networks.

Time crystals are an exotic newcomer to physics, and researchers have much to learn about their unusual properties. First proposed in 2012, and finally observed experimentally in 2017, time crystals evolve continually as structures that repeat regularly in time. This is analogous to normal crystals, which have structures that repeat regularly in space. A normal crystal breaks translational symmetry in space because it is not the same everywhere in the crystal (some locations have atoms, while locations are empty space).  Similarly, time crystals break translational symmetry in time, with the structure changing as a function of time.

When time crystals were first proposed there was a fair amount of debate about whether they could exist in nature. More recently, theory and experiment have shown that some non-equilibrium quantum systems driven by a periodic external force can become “discrete time crystals” (DTCs).

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