Diffusion of an Active Particle Bound to a Generalized Elastic Model: Fractional Langevin Equation

We investigate the influence of a self-propelling, out-of-equilibrium active particle on
generalized elastic systems, including flexible and semi-flexible polymers, fluid membranes, and
fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the frac-
tional Langevin equation governing the dynamics of the active particle, as well as that of any other
passive particle (or probe) bound to the elastic system. This equation analytically demonstrates
how the active particle dynamics is influenced by the interplay of both the non-equilibrium force
and of the viscoelastic environment. Our study explores the diffusional behavior emerging for both
the active particle and a distant probe. The active particle undergoes three different surprising and
counter-intuitive regimes identified by the distinct dynamical time-scales: a pseudo-ballistic initial
phase, a drastic decrease in the mobility, and an asymptotic subdiffusive regime.