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→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 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.Comment: Accepted in J. Chem. Phy