Random organization and non-equilibrium hyperuniform fluids on a sphere

Randomly organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales such as 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 → 0) ∼ (l/R)^0.45 and S(l → 0) ∼ l(l + 1)/R², 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 by 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.