Density and Current Fluctuations for Run-and-Tumble Particles With and Without Interactions

We study density and current fluctuations in a one-dimensional gas of run-and-tumble particles (RTPs), whose intrinsic velocities switch between two opposite values at a constant rate. We consider particles with and without pair interactions, including regularized Riesz gases, and also obtain corresponding results for Brownian particles. By linearizing the Dean-Kawasaki (DK) equations around a homogeneous stationary state, we compute density correlations and the variance of the integrated current through the origin. For repulsive Riesz interactions decaying as $1/|x|^s$ with $s>0$, this variance grows at long times as $t^{1/2}$ for $s>1$, but as $t^{s/(1+s)}$ for $0