Tagged particle behavior in a harmonic chain of direction reversing active Brownian particles

Abstract

We study the tagged particle dynamics in a harmonic chain of direction reversing active Brownian particles, with spring constant $k$, rotation diffusion coefficient $D_{\text{r}}$, and directional reversal rate $\gamma$. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time scales, $k^{-1}$, $D_{\text{r}}^{-1}$ and ${\gamma }^{-1}$, the strength of spring constant $k$ relative to $D_{\text{r}}$ and $\gamma$ gives rise to different coupling limits and for each coupling limit there are short, intermediate, and long time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth $t^{\nu }$, where the value of the exponent $\nu$ depends on the specific regime. For a quenched initial orientation, the exponent $\nu$ crosses over from $3$ to $1/2$, via intermediate values $5/2$ or $1$, depending on the specific coupling limits. On the other hand, for the annealed initial orientation, $\nu$ crosses over from $2$ to $1/2$ via an intermediate value $3/2$ or $1$ for strong coupling limit and weak coupling limit respectively. An additional time scale $t_N=N^2/k$ emerges for a system with a finite number of oscillators $N$. We show that the behavior of the tagged particle variance across $t_N$ can be expressed in terms of a crossover scaling function, which we find exactly. Finally, we characterize the stationary state behavior of the separation between two consecutive particles by calculating the corresponding spatio-temporal correlation function.

References in corpus (17)

• A self-propelled particle in an external potential: is there an effective temperature?
• Large Deviations in Single File Diffusion
• Selective and Collective Actuation in Active Solids
• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Active Brownian Motion with Directional Reversals
• Tagged Particle Correlations in the Asymmetric Simple Exclusion Process: Finite Size Effects
• AOUP in the presence of Brownian noise: a perturbative approach
• Time-dependent properties of interacting active matter: dynamical behavior of one-dimensional systems of self-propelled particles
• Exact correlations in a single file system with a driven tracer
• Strong Mobility in Weakly Disordered Systems
• Diffusion of tagged particles in a crowded medium
• Duality relations in single-file diffusion
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Stochastic thermodynamics of a tagged particle within a harmonic chain
• Tagged particle diffusion in one-dimensional systems with Hamiltonian dynamics - II
• Long time behavior of run-and-tumble particles in two dimensions

Cited by in corpus (3)

• Tracer dynamics in an interacting active bath: fluctuations and energy partition
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• From Attraction to Repulsion: Emergent Interactions in Harmonically Coupled Active Binary System