At each sampling time instant, one observes system output and action to form discrete-time rewards. The sampled input-output data are collected along the trajectory of the dynamical system in ...

Physical systems become inherently more complicated and difficult to produce in a lab as the number of dimensions they exist in increases—even more so in quantum systems. While discrete time crystals ...

Crystals are nature's most orderly substances. Inside them, atoms and molecules are arranged in regular, repeating structures, giving rise to solids that are stable and rigid—and often beautiful to ...

Time crystals break time-translational symmetry rather than spatial symmetry, as ordinary crystals do. Peter Hannaford and Krzysztof Sacha look at how this exotic state could have similar applications ...