Giant density fluctuations in locally hyperuniform states

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.

💡 Research Summary

The paper investigates the coexistence of two seemingly contradictory density‑fluctuation phenomena in active matter: giant number fluctuations (GNF) that arise in orientationally ordered active systems, and hyperuniformity, a suppression of large‑scale density fluctuations that appears near absorbing phase transitions. To bridge these behaviors the authors introduce a minimal “nematic random organization model” (NROM). In this model particles carry a nematic director that updates via a Vicsek‑type rule with noise σ, but particles are only motile when they overlap with at least one neighbor; overlapping particles then move a fixed step δ₀ along their director (with a random sign). This rule couples activity to the local environment, mimicking “contact‑triggered motility”.

Simulations are performed in two dimensions with parameters σ=0.1, δ₀=0.3, interaction range Rₐₗ=1, particle diameter D=0.46, and system size up to L≈500. The control variables are the packing fraction φ and the step size δ₀. As in the classic Random Organization Model (ROM), the system exhibits an absorbing phase transition at a critical packing fraction φ_c≈0.30984. For φ<φ_c the activity A (fraction of overlapping particles) decays to zero and the configuration freezes; for φ>φ_c the activity reaches a steady non‑zero value ⟨A⟩∝(φ−φ_c)^β with β≈0.63, consistent with the conserved directed percolation (CDP) universality class. Importantly, for φ>φ_c the particles also develop strong nematic order, quantified by the scalar order parameter S>0.

Density fluctuations are quantified by the variance ⟨Δn²⟩ of particle number n inside boxes of linear size ℓ. Plotting ⟨Δn²⟩ versus the mean ⟨n⟩ reveals two anomalous regimes. At intermediate ℓ the scaling exponent α_hu≈0.77 (<1) signals hyperuniformity, matching the exponent found in the ROM. At larger ℓ the exponent α_gnf≈1.65 (>1) indicates GNF, identical to that of 2‑D active nematics. The crossover length ξ separating the two regimes grows as φ approaches φ_c from above, following ξ∝(φ−φ_c)^{-μ} with μ≈0.625. A similar crossover is observed in the static structure factor S(q): for very small wavevectors q the spectrum diverges with a negative exponent λ_gnf (GNF), while for intermediate q it follows a positive exponent λ_hu (hyperuniformity). Rescaling S(q) by appropriate powers of Δφ collapses data from different φ onto a universal curve, confirming the critical crossover.

To rationalize these findings the authors construct a continuum hydrodynamic theory involving three fields: the conserved density ρ(r,t), the nematic order tensor Q(r,t), and the activity density A(r,t). The particle current is taken as J = D_ρ∇A + χ₁ Q·∇A + χ₂ A∇·Q, where the last two terms are the curvature‑driven currents familiar from active nematics. The density obeys a continuity equation with a noise term proportional to √A, while the activity follows a CDP‑type reaction–diffusion equation (∂_t A = ∇·J + (κρ−a)A − λA² + noise). The nematic tensor evolves via a Landau‑de Gennes equation with an additional term χ₃∇∇A coupling activity gradients to nematic curvature. Linearizing around the homogeneous ordered state (ρ=ρ₀, A=A₀∝Δφ, Q=Q₀) and Fourier transforming yields an analytical expression for the structure factor:

S(q) ∝ (1−cos4θ) λ²χ₂² σ_Q² /