Ordering and dynamics of active matter systems on static and dynamic periodic optical substrates

Self-propelled particles are found in many biological systems as well as in numerous synthetic systems where self-motile colloids and artificial swimmers have recently been realized. These active systems exhibit a variety of process not found in equilibrium systems. Most studies of active matter have been performed with smooth landscapes; however, there is an increasing amount of work on active matter coupled to ordered or disordered substrates. Due to the size scale of the active particles, suitable random, periodic, or quasiperiodic substrates could be made optically. Here we present recent results for active matter on periodic substrates and discuss some future directions. We also enumerate many of the active matter versions of nonactive systems that could be realized with periodic substrates, including an active matter glass, commensurate-incommensurate transitions, solitons, and sliding states. We show that the driven dynamics of active matter can produce directional locking on periodic substrates. Finally, we discuss the possibility of introducing a dynamical substrate in order to create active matter versions of classical time crystals.