Can mobility induce orders in active oscillators on a substrate

We study the coherent collective diffusive motion of neraly phase-ordered active oscillators on a substrate. We construct the hydrodynamic theory of this system, and use it to make many testable predictions. We find that for a wide range of parameters this system can be stable with orientational order generically stronger or weaker than quasi long range order (QLRO) in different regions of the parameter space. The number density fluctuations correspondingly are either generally hyperuniform, or giant. In the remaining parameter space, the system becomes unstable. Simulations of an equivalent agent-based lattice-gas model support the predictions of the hydrodynamic theory on the phase-ordered states. Our theory forms the basis for theoretical understanding of wide-ranging phenomena, e.g., oscillator synchronization in networks with evolving connections and active superfluids.