Hyperuniform interfaces in non-equilibrium phase coexistence

Abstract

We show that long-wavelength interfacial fluctuations are strongly suppressed in non-equilibrium phase coexistence between bulk hyperuniform systems. Using simulations of three distinct microscopic models, we demonstrate that hyperuniform interfaces are much smoother than equilibrium ones, with a universal reduction of height fluctuations at large scale. We derive a non-equilibrium interface equation from the field theory of the bulk order parameter, and predict a reduction in height fluctuations, $S_h(\mathbf{k})\equiv ⟨|h(\mathbf{k}){|}^2⟩\sim |\mathbf{k}{|}^{-1}$, in stark contrast to equilibrium capillary wave theory where $S_h(\mathbf{k})\sim |\mathbf{k}{|}^{-2}$. Our results establish a new universality class for non-equilibrium interfaces, highlighting the fundamental role of suppressed bulk fluctuations in shaping interfacial dynamics far from equilibrium.