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

Abstract

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 fractional 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.

Regular and anomalous diffusion: I. Foundations

“…Over two centuries after the pioneering observation of Ingenhousz, the multidisciplinary field of diffusion is bustling with scientific activity. Examples of recent research include: tracer diffusion [61][62][63][64][65]; polymer diffusion [66][67][68][69][70]; heterogeneous diffusion [71][72][73][74][75]; non-Gaussian diffusion [76][77][78][79][80][81][82][83]; random diffusivity [84][85][86][87][88][89][90][91][92]; diffusion of active particles [93][94][95][96][97][98]; diffusion and Bayesian analysis [99][100][101]; diffusion and machine learning [102][103][104][105][106]; and stochastic resetting of diffusion [107]…”