Dynamical crossovers and correlations in a harmonic chain of active particles

Abstract

We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSD) and space-time correlations through Green's function techniques and numerical simulations. Depending on chain characteristics, i.e., different time scales determined by interaction stiffness and persistence of activity, tagged-particle MSD exhibit ballistic, diffusive, and single-file diffusion (SFD) scaling over time, with crossovers explained by our analytic expressions. Our results reveal transitions in bulk particle displacement distributions from an early-time bimodal to late-time Gaussian, passing through regimes of unimodal distributions with finite support and negative excess kurtosis and longer-tailed distributions with positive excess kurtosis. The distributions exhibit data collapse, aligning with ballistic, diffusive, and SFD scaling in the appropriate time regimes. However, at much longer times, the distributions become Gaussian. Finally, we derive expressions for steady-state static and dynamic two-point displacement correlations, consistent with simulations and converging to equilibrium results for small persistence. Additionally, the two-time stretch correlation extends to longer separation at later times, while the autocorrelation for the bulk particle shows diffusive scaling beyond the persistence time.

References in corpus (13)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Heat Transport in low-dimensional systems
• Swarming and swirling in self-propelled polar granular rods
• A self-propelled particle in an external potential: is there an effective temperature?
• Emergent vortices in populations of colloidal rollers
• 'Fuelled' motion: phoretic motility and collective behaviour of active colloids
• Single-File diffusion in a Box
• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Non-crossing run-and-tumble particles on a line
• Exact Solution of Two Interacting Run-and-Tumble Random Walkers with Finite Tumble Duration
• Whirligig Beetles as Corralled Active Brownian Particles
• Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles

Cited by in corpus (5)

• Single-File Diffusion of Active Brownian Particles
• Tracer dynamics in an interacting active bath: fluctuations and energy partition
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• From Attraction to Repulsion: Emergent Interactions in Harmonically Coupled Active Binary System