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, $S_h(\boldsymbol k)\equiv \langle |h(\boldsymbol k)|^2\rangle\sim |\boldsymbol k|^{-1}$, in stark contrast to equilibrium capillary wave theory where $S_h(\boldsymbol k)\sim |\boldsymbol k|^{-2}$. 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.

Figures (3)

• Figure 1: Binary-mixture with active collisions. (a) Snapshot of a fully phase-separated $AB$ mixture evolving under equilibrium Langevin dynamics with a square well potential interaction. The parameters are: $T/U=-0.8$, $\sigma_U/\sigma=1.6$, $m(\sigma\Gamma)^2/T=0.075$, $N\pi\sigma^2/(4L_xL_y)=0.55$ and $L_x=1.81L_y$, where $T$ is the kinetic energy of the system per particle. (b) Snapshot for the non-equilibrium system governed by Eqs. (\ref{['eq: collision rule RanNi']}, \ref{['eq: damping']}) with attraction. All parameters are identical to those in the equilibrium case without thermostat, and $\Delta E$ is chosen to match the kinetic energy of the equilibrium system. (c) Interface static height correlation functions for the two cases. (d) Radially averaged structure factors in the bulk. (e) Time evolution of $W^2$ for various system size for both models starting from a flat initial interface, averaged between 80 and 900 independent realizations. (f) Time to reach steady state $\tau_{\rm ss}$ as a function of the short box length $L \equiv L_y$ for the systems in (e).
• Figure 2: Random organization models. (a-b) Snapshots of a phase-separated mixtures evolving under BRO (a) and CBRO (b) dynamics. The parameters are: $\sigma_2/\sigma_1=1.4$, $\epsilon_1/\sigma_1=0.5$, $\epsilon_2/\sigma_1=0.1$, $N=5\times10^4$, $L=256\sigma_1$. (c) Interface static height correlation functions. (d) Radially averaged structure factors in the bulk. Results are averaged over 20 independent realizations.
• Figure 3: Mono-component system. (a) Snapshot with particles colored by velocity magnitude. (b) Probability distribution of height displacement $h$. The dashed line is a Gaussian fit. Inset: zoom on the distribution tail to reveal the asymmetry of the distribution with measured skewness $\kappa_3\simeq0.045$ and excess kurtosis $\kappa_4\simeq0.031$ for this system size. (c) Structure factor of bulk coexisting liquid and gas phases. (d) Static height correlation. Parameters are $\delta E / \delta E_0 = 2 \times 10^3$, $\beta = 10$, $\tau_r\Gamma = 0.2$, $\delta E_0/m(\sigma\Gamma)^2=10/36$, $L_x=1.81L_y=383\sigma$ and $N\pi\sigma^2/(4L_xL_y)=0.31$ .