Random organization and non-equilibrium hyperuniform fluids on a sphere

Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely a spherical surface. We find that the random organization on a spherical surface behaves similar to that in two dimensional Euclidean space, and the absorbing transition on a sphere also belongs to the conserved directed percolation universality class. Moreover, the reciprocal activation can also induce a non-equilibrium hyperuniform fluid on a sphere. The spherical structure factor at the absorbing transition and the non-equilibrium hyperuniform fluid phases are scaled as $S(l \rightarrow 0) \sim (l/R)^{0.45}$ and $S(l \rightarrow 0) \sim l(l+1)/R^2$, respectively, which are both hyperuniform according to the definition of hyperuniformity on a sphere with $l$ the wave number and $R$ the radius of the spherical surface. We also consider the impact of inertia in realistic hyperuniform fluids, and it is found only adding an extra length-scale, above which hyperuniform scaling appears. Our finding suggests a new method for creating non-equilibrium hyperuniform fluids on closed manifolds to avoid boundary effects.