Figure 2: Normalized velocity variance for a 1d system of many interacting active particles.

Symbols are the results of numerical simulations for several values of τ and D (see legend). Dashed lines are the theoretical velocity variances obtained by averaging Eq. (3) over the coordinates obtained numerically. Thick lines are the result of a homogenous density approximation. Dashed-dotted lines represent the small-τ approximation connecting the variance to the pair distribution function. Dotted lines are the velocity variances obtained by mapping the system onto a harmonic model.