Reduced density fluctuations via anti-aligning in active matter

We highlight the importance of long-range correlations in active matter systems of self-propelling particles even in the absence of global order or steric interactions by demonstrating that long-range density fluctuations are reduced. We show this analytically for a one-dimensional lattice process employing a Poisson representation. Within this framework, we are able to derive the fluctuating hydrodynamics for the Poisson fields. The emergent imaginary noise indicates the non-Poissonian nature of the number fluctuations and manifests in a non-trivial structure factor $S(k)$ which we are computing analytically. Numerically, we corroborate the relevance of these findings for off-lattice Vicsek-type models with anti-aligning interactions for which we observe apparent non-universal hyperuniformity which we suggest to interpret as a reduction with integer power-law to a finite value.