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 semiflexible 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 demonstrates analytically 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 counterintuitive regimes identified by the distinct dynamical time-scales: a pseudo-ballistic initial phase, a drastic decrease of the mobility and an asymptotic subdiffusive regime.

References in corpus (18)

• Self-motile colloidal particles: from directed propulsion to random walk
• Motility-Induced Phase Separation
• Spontaneous motion in hierarchically assembled active matter
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Generalized energy equipartition in harmonic oscillators driven by active baths
• How does a flexible chain of active particles swell?
• Unusual swelling of a polymer in a bacterial bath
• Activity induced collapse and re-expansion of rigid polymers
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Generalized Elastic Model yields Fractional Langevin Equation
• Active Ornstein-Uhlenbeck model for self-propelled particles with inertia
• Flow-Induced Helical Coiling of Semiflexible Polymers in Structured Microchannels
• Anomalous diffusion for active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory
• Behavior of active filaments near solid-boundary under linear shear flow
• Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach
• Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity
• Unusual Response to a Localized Perturbation in a Generalized Elastic Model