Singular Density Correlation in Three-Dimensional Chiral Active Fluids

In this chapter, we investigate density fluctuations in three-dimensional chiral active fluids using a simple model of helical self-propelled particles. Numerical simulations demonstrate that helicity induces an anisotropic pattern and a singularity in the static structure factor, that is, the density correlation function in Fourier space, in the low-wave-number limit. Moreover, in the limit of infinite persistence time, the system exhibits hyperuniformity in the direction perpendicular to the chiral torque, while giant density fluctuations emerge along the parallel direction. We then construct a fluctuating hydrodynamic theory for this system to describe the observed singular behavior. A linear analysis of the resulting equations yields an analytical expression for the static structure factor, which qualitatively agrees with the numerical results.