Active mobile oscillators on a substrate: Density fluctuations and phase ordering

Astik Haldar, Apurba Sarkar, Swarnajit Chatterjee, Abhik Basu

Published 2021-05-09Version 1

We explore the generic long wavelength properties of a collection of nearly phase-ordered active oscillators, which rotate actively in response to local density fluctuations and local phase differences, on a solid substrate. We investigate this system by constructing and studying the hydrodynamic theory of the system. This theory shows that such a system can be stable over a wide range of the model parameters. In different regions of the phase space where the system is stable, it shows phase ordering that is generically either stronger than the conventional quasi long range order (QLRO) together with "hyperuniform" number fluctuations, or phase ordering weaker than QLRO along with giant number fluctuations. These are characterized by the breakdown of conventional dynamic scaling by logarithmic modulations. In other parameter regimes, the system becomes unstable with eventual loss of any phase ordering beyond a finite (small) system size. We also construct an equivalent agent-based lattice-gas model. Numerical simulations of this model are used to support our results on phase ordering.