Pattern formation and dynamics of particles with competing interactions on periodic optical substrates

There is a large class of particle like systems, including cold atoms, colloidal particles, magnetic particles, and active matter, that can be coupled to a periodic substrate. Such substrates may be effectively one- or two-dimensional and can be created by optical means. A variety of commensuration effects can occur when the spacing between particles matches the periodicity of the substrate. In addition, a number of interesting dynamic effects arise under dc and ac driving, where the nature of the particle flow depends on the commensuration conditions. Here, we consider particles with competing long-range repulsive and short-range attractive interactions driven over a quasi-one-dimensional periodic substrate. In the absence of the substrate, the particles adopt crystalline, stripe, or bubble orderings; however, in the presence of the substrate, a wide variety of novel static and dynamic phases can arise.