Beyond the Markovian limit: Exact solutions for active motion in a power-law viscoelastic bath

Abstract

Active particles from bacteria to synthetic microswimmers often navigate viscoelastic media with complex relaxation dynamics. The classical active Brownian model that assumes instantaneous friction is clearly not applicable to describe such motility, while the non-Markovian processes combined with viscoelasticity are relatively unexplored. Here, we develop an analytical theory for an active particle in a power-law viscoelastic medium by solving coupled non-Markovian generalized Langevin equations for translational and rotational degrees of freedom. The viscoelastic memory results in novel phenomena such as fractional short-time transport, enhanced long-time persistence, and de-correlation of the instantaneous force and the swimmer orientation. We demonstrate that the memory kernel controls the anomalous scaling exponents, while the activity determines the crossover between sub-diffusive, ballistic and diffusive regimes. Our work provides a framework for theoretical description of biological and synthetic micro swimmers in complex biological and polymeric environments.

References in corpus (16)

• Novel type of phase transition in a system of self-driven particles
• The hydrodynamics of swimming microorganisms
• Self-motile colloidal particles: from directed propulsion to random walk
• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Anomalous transport in the crowded world of biological cells
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Collective motion of self-propelled particles interacting without cohesion
• Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations
• Effective Interactions in Active Brownian Suspensions
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
• Fractional Langevin Equation: Over-Damped, Under-Damped and Critical Behaviors
• Small Obstacle in a Large Polar Flock
• Dynamic Clustering of Active Rings
• Active Brownian particles in power-law viscoelastic media