Giant density fluctuations in locally hyperuniform states

Abstract

Systems driven far from equilibrium may exhibit anomalous density fluctuations: active matter with orientational order display giant density fluctuations at large scale, while systems of interacting particles close to an absorbing phase transition may exhibit hyperuniformity, suppressing large-scale density fluctuations. We show that these seemingly incompatible phenomena can coexist in nematically ordered active systems, provided activity is conditioned to particle contacts. We characterize this unusual state of matter and unravel the underlying mechanisms simultaneously leading to spatially enhanced (on large length scales) and suppressed (on intermediate length scales) density fluctuations. Our work highlights the potential for a rich phenomenology in active matter systems in which particles' activity is triggered by their local environment, and calls for a more systematic exploration of absorbing phase transitions in orientationally-ordered particle systems.

Figures (3)

• Figure 1: (a) Sketch of the phase diagram for the ROM model showing the active and passive phases in the volume fraction $\phi$ -- step size $\delta_0$ plane, inspired by Fig. 1 in tjhung2015. (b) Sketch of the phase diagram for active nematics showing the isotropic and nematically ordered phases in the density $\rho$ -- noise amplitude $\sigma$ plane, inspired by Fig. 2 in ngo2014 (blue shaded area: phase-separated nematic state). The NROM model: (c) Activity $A$ (data collapse shown in the inset) and (d) scalar nematic order $S$ versus time, for several packing fractions $\phi$. Data are averaged over more than 40 realizations. (e) Steady-state activity $\langle A \rangle$ versus packing fraction $\phi$.
• Figure 2: (a) Number fluctuations $\langle \Delta n^2 \rangle_{\ell}= \langle n^2 \rangle_{\ell} - \langle n \rangle_{\ell}^2$ versus $\langle n \rangle_{\ell}$ in logarithmic scale for several packing fractions $\phi > \phi_\mathrm{c} = 0.30984$. (b) Same data, rescaled as $\langle \Delta n^2 \rangle_{\ell} / \Delta \phi^{-0.75}$ versus $\langle n \rangle_{\ell}/\Delta \phi^{-1.25}$. (c) Structure factor $S(q)$ for several values of $\phi > \phi_\mathrm{c}$ in logarithmic scale. (d) Same data, rescaled as $S(q)/\Delta \phi^{0.55}$ versus $q/\Delta \phi^{0.625}$. For $\phi =0.353, 0.345, 0.340, 0.328$ system size $L=516$ and for $\phi = 0.320, 0.315$ system size $L=774$.
• Figure 3: Density fields of steady-state configurations from the NROM model [top row, (a)--(b)] and of a Poissonian realization [bottom row (c)--(d)] with same system size $L = 2850$ and packing fraction $\phi =0.34327$, obtained with two different values of the coarse-graining length $s$: $s=3$ [(a) and (c)] and $s=30$ [(b) and (d)].