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 ...

Structures known as 'time crystals' -- which repeat in time as conventional crystals repeat in space -- have recently captured the interest and imagination of researchers across disciplines. The ...

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 ...