Tracer dynamics in one dimensional gases of active or passive particles

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.

arXiv comment32 pages, 26 figures

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• Rectification in a mixture of active and passive particles subject to a ratchet potential
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• Tracer dynamics in an interacting active bath: fluctuations and energy partition
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• Lecture notes on large deviations in non-equilibrium diffusive systems
• Jamming of active particles in narrow pores: Implications for ratchet effect and diffusion coefficient
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Effective diffusion of a tracer in active bath: a path-integral approach