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 ...

Scientists believe that time is continuous, not discrete—roughly speaking, they believe that it does not progress in "chunks," but rather "flows," smoothly and continuously. So they often model the ...

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 ...

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete ...

Discrete time crystals are non-equilibrium many-body phases of matter characterized by spontaneously broken discrete time-translation symmetry under periodic driving. At sufficiently high driving ...