Conservation laws and slow dynamics determine the universality class of interfaces in active matter

TL;DR

The paper addresses non-equilibrium interfacial fluctuations in active matter, where conventional equilibrium universality can fail. It introduces a minimal active hard-disk model, driven by collision-based energy exchange and a Langevin bath, to realize three non-equilibrium liquid–gas universality classes predicted for interfaces: the $|oldsymbol q|$KPZ class, the wet-$|oldsymbol q|$KPZ class, and a hyperuniform-like (HU) class, with each class selected by distinct conservation laws and slow hydrodynamic modes. Moreover, it uncovers a fourth, previously overlooked universality class arising when the dense phase undergoes slow crystalline or glassy dynamics, evidenced by changes in the static roughness exponent $oldsymbol{\chi}$ (e.g., $oldsymbol{\chi} o 0$ for crystalline and $oldsymbol{\chi} o oldsymbol{0.25}$ for glassy dense phases) and corresponding dynamic behavior. The results show that conservation laws and slow bulk dynamics fundamentally reshape interfacial statistics, and they point to vibrated granular systems as experimentally accessible platforms for probing these non-equilibrium interfacial phenomena. Formally, the classes exhibit distinct exponents: $z^{|oldsymbol q| m KPZ} o 2.2$–$2.8$, $oldsymbol{\chi}^{|oldsymbol q| m KPZ} o 0.3$–$0.4$; $z^{ m wet}=1$, $oldsymbol{\chi}^{ m wet}=1$; and $oldsymbol{\chi}^{ m HU}=0$, $z^{ m HU}=3$, with additional slow-dynamics-induced regimes altering $oldsymbol{\chi}$ as described above.

Abstract

While equilibrium interfaces display universal large-scale statistics, interfaces in phase-separated active and driven systems are predicted to belong to distinct non-equilibrium universality classes. Yet, such behavior has proven difficult to observe, with most systems exhibiting equilibrium-like fluctuations despite their strongly non-equilibrium microscopic dynamics. We introduce an active hard-disk model that contrary to self-propelled models, displays clear non-equilibrium interfacial scaling and observe for the first time, the $|\boldsymbol q|$KPZ and wet-$|\boldsymbol q|$KPZ universality classes while revealing a new, previously overlooked universality class arising in systems with slow crystalline or glassy dynamics. These distinct classes are selected by conservation laws and slow hydrodynamic modes.

Figures (8)

• Figure 1: Simulations of three qualitatively distinct systems based on Eqs. \ref{['eq: time evol']} and \ref{['eq: energy change at collision']}. In the first row, only the density field is conserved, in the second row, momentum is also conserved and in the last row only the density field is conserved but the mesoscopic noise conserves the center-of-mass of the system. a), f), and k) show snapshots centered on the interface, with particles colored by velocity. Panels b), g), and l) display the steady-state static height correlations as a function of wavenumber. c), h), and m) show the time evolution of the interface width squared, starting from a flat interface, for various system sizes. d), e), i), j), n), and o) show the system-size dependence of the coarsening time and steady-state width squared $W^2_{ss}\equiv W^2(t\to\infty)$. The averages are computed over 50 to 1000 independent initial configurations, with at least 300 snapshots taken for each configuration. In a-e), we set $T/\hat{E}=0.05$, $\Gamma/\hat{\tau}=0.05$, $\tau_r/\hat{\tau}=4$, $\delta E_0/\hat{E} = 0.0025$, $\delta E/\hat{E} = 15$, $\beta = 10$, $\alpha = 0.99$ and $L_x=2L_y$. For f-j), we set $\Gamma/\hat{\tau}=0$, $\tau_r/\hat{\tau}=3$, $\delta E_0/\hat{E} = 0.0125$, $\delta E/\hat{E} = 25$, $\beta = 10$, $\alpha = 0.95$ and $L_x=8L_y$. For k-o), we set $T/\hat{E}=0$, $\Gamma/\hat{\tau}=0.075$, $\tau_r/\hat{\tau}=3$, $\delta E_0/\hat{E} = 0.0125$, $\delta E/\hat{E} = 25$, $\beta = 10$ and $\alpha = 0.95$, $L_x=2L_y$.
• Figure 2: Simulations of a liquid-solid interface in a system with momentum conservation (top) and without momentum conservation (bottom). a), d) and b), e) are the local packing fraction and bond orientational order profiles normal to the interface, respectively. c) and f) are the static height correlations with respect to the wavevector showing a scaling change when the dense phase crystallizes. The parameters, except the ones explicitly varied, are the same as in Fig. \ref{['fig: recap']}. For the system with $\Gamma = 0$, $N\simeq 2\times 10^5$, for the other $N\simeq 8\times10^4$.
• Figure 3: Simulations of a liquid–glass interface in a binary hard-disk mixture with momentum conservation. a) Static height correlations versus wavevector show a change in scaling as the dense phase becomes glassy, as measured in the inset showing the mean-square displacement (MSD) of homogeneous systems at the corresponding dense-phase densities, plotted against time normalized by the collision rate $\omega_{\rm coll}$. b–d) Representative interface profiles for low, intermediate, and high $\delta E_0$. All parameters match those in Fig. \ref{['fig: recap']}, except for the varied $\delta E_0$ and $\alpha = 0.9$. $2.5\times10^5\leq N\leq 3.5\times10^5$. The mixture is equimolar with sizeratio 0.7.
• Figure 4: Initial and late time configuration of a typical system.
• Figure 5: Quantification of the finite size effects for the system with $\Gamma= 0$ and $L_y=500\sigma$. a) Static height correlation function for various system size. b) Coarsening of these different system sizes with time. The parameters are the same as the one used in Fig. \ref{['fig: recap']} of the main text for the system with $\Gamma=0$.