Hidden order in active nematic defects

Abstract

Hyperuniformity and giant number fluctuations represent opposite ends in a spectrum of statistical correlations found in physical systems outside of thermal equilibrium. Dynamic phase transitions exhibit critical points that are hyperuniform, while anomalously large fluctuations are often quoted as a hallmark of active matter. Here, we show that the apparently disordered state of active nematic defects exhibits suppression of fluctuations on scales as large as the system size, reminiscent of what is seen for ordered lattices. Modeling the nematic defects in terms of continuum densities, we show that their distribution becomes asymptotically hyperuniform in the limit where their proliferation is solely driven by activity, rather than by thermal fluctuations. When both effects are at play, the resultant hyperuniform structure is limited to a finite range of length scales, [Formula: see text], with [Formula: see text] as thermal unbinding is suppressed. The system of active nematic defects can therefore be said to possess hidden order across scales provided ℓ is comparable to the system size. This organization is most pronounced when considering the subpopulation of either the positive or the negative defects, illustrating lack of multihyperuniformity. Our experimental findings are supported by hydrodynamic theory and agent-based simulations, which further allow elucidating the role of both creation/annihilation of defect pairs and of their mutual repulsion and attraction in achieving hyperuniformity.

Keywords: active matter; hyperuniformity; nematic defects; number fluctuations.