Tracer dynamics in the active random average process

We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable sigma(t) that can alternate between two values, +/- 1, at a constant rate gamma. Physically, the value of sigma(t) dictates the direction of motion of the corresponding particle and, for finite gamma, every particle performs non-Markovian active dynamics. Herein, we study the effect of this non-Markovian behavior in the fluctuations and correlations of the positions of tracer particles. We analytically show that the variance of the position of a tagged particle grows sub-diffusively as similar to zeta qt at large times for the quenched uniform initial conditions. While this sub-diffusive growth is identical to that of the Markovian/non-persistent RAP, the coefficient zeta q is rather different and bears the signature of the persistent motion of active particles through higher-point correlations (unlike in the Markovian case). Similarly, for the annealed (steady-state) initial conditions, we find that the variance scales as similar to zeta at at large times, with the coefficient zeta a once again different from the non-persistent case. Although both zeta q and zeta a individually depart from their Markovian counterparts, their ratio zeta a/zeta q is still equal to 2 , a condition observed for other diffusive single-file systems. This condition turns out to be true even in the strongly active regimes, as corroborated by extensive simulations and calculations. Finally, we study the correlation between the positions of two tagged particles in both quenched uniform and annealed initial conditions. We verify all our analytical results using extensive numerical simulations.