Hydrodynamics of Random-Organizing Hyperuniform Fluids

Disordered hyperuniform structures are locally random while uniform like crystals at large length scales. Recently, an exotic hyperuniform fluid state was found in several non-equilibrium systems, while the underlying physics remains unknown. In this work, we propose a non-equilibrium (driven-dissipative) hard-sphere model and formulate a hydrodynamic theory based on Navier-Stokes equations to uncover the general mechanism of the fluidic hyperuniformity (HU). At a fixed density, this model system undergoes a smooth transition from an absorbing state to an active hyperuniform fluid, then to the equilibrium fluid by changing the dissipation strength. We study the criticality of the absorbing phase transition. We find that the origin of fluidic HU can be understood as the damping of a stochastic harmonic oscillator in $q$ space, which indicates that the suppressed long-wavelength density fluctuation in the hyperuniform fluid can exhibit as either acoustic (resonance) mode or diffusive (overdamped) mode. Importantly, our theory reveals that the damping dissipation and active reciprocal interaction (driving) are two ingredients for fluidic HU. Based on this principle, we further demonstrate how to realize the fluidic HU in an experimentally accessible active spinner system and discuss the possible realization in other systems.