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 an RTP tracer during a ballistic run.
Highlights
The problem of a tagged particle in single-file diffusion has been of interest to physicists for more than five decades [1, 2, 3, 4, 5, 6], since its inception in the study of transport through ion channels in cell membranes [7]
For the two fully passive systems, the only hardcore interaction that matters for tracer dynamics is the one between tracer and environment, which is present in both cases
We have studied the behaviour of tracers in hardcore interacting and non-interacting media in one-dimension for all eight combinations (Table 1) of active and passive tracer and environment particles
Summary
The problem of a tagged particle in single-file diffusion has been of interest to physicists for more than five decades [1, 2, 3, 4, 5, 6], since its inception in the study of transport through ion channels in cell membranes [7]. We identify eight separate problems (see Table 1), depending on whether the environmental particles are hardcore or noninteracting, whether they are active (RTP) or passive (Brownian), and whether the hardcore tracer is itself active or passive Several of these cases have been studied before, but to the best of our knowledge, they are yet to be systematically compared under a common umbrella. We use numerical simulations to analyse and compare the eight problems shown, which we identify by a three-letter short-hand code whose first letter refers to the environment particles as active (RTPs, A) or passive (Brownian walkers, P); the second letter does the same for the tracer; and the third labels whether the environment particles are mutually non-interacting (N) or hardcore (H). Cases APH, APN, PAN, like PAH, all involve mixtures of active and passive particles; these are well studied in terms of phase separation [41, 42] but not single-file diffusion.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Mechanics: Theory and Experiment
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
