Dynamic hyperuniformity of driven suspensions

We show that externally forced particles in a suspension self-organize hyperuniformly in certain directions relative to the force. For this phenomenon to occur, the force-induced coupling between the concentration of particles and their velocity field should satisfy three conditions : (i) it should be long-ranged, decaying with distance r as 1/r^β, with β smaller than the dimensionality d; (ii) it should have a finite divergence, i.e., the flow of particles should not conserve volume; (iii) it should not be inversion-symmetric. These conditions are fulfilled, for example, for particles which tend to align with the force, or in the presence of a steady concentration gradient. The directions of hyperuniformity depend on the specific coupling. The structure factor for wavevectors q along these directions tends to zero for small q as q^α, α = d – β. We check these analytical results in a simple two-dimensional simulation, showing that they are robust against particle collisions and diffusion.