Tracer dynamics in one dimensional gases of active or passive particles

TL;DR

This paper investigates the complex dynamics of tracer particles in one-dimensional active and passive particle systems, revealing subdiffusive behavior and the influence of interactions and environment on tracer motion.

Contribution

It provides a detailed analysis of tracer dynamics in 1D active/passive systems, highlighting new subdiffusive regimes and effects of interactions not previously characterized.

Findings

Active tracers in active environments show $t^{1/4}$ subdiffusion.

Passive tracers exhibit caging effects at higher densities.

Active-in-passive interactions lead to snowplough effects and complex behaviors.

Abstract

We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system - this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as $t^{1/4}$ with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any $t^{1/4}$ regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a `snowplough' effect whereby a large pile of diffusive environmental particles accumulates in front of a RTP tracer during a ballistic run.