Motion of active tracer in a lattice gas with cross-shaped particles

Abstract

We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations. We show that the properties of the passive system alone do not adequately describe even this simple system of a single non-rotating active tracer. For large activity and low density, we develop an approximation for v. For the case where the tracer undergoes rotational diffusion independent of its neighbors, we relate its diffusion coefficient to the thermal diffusion coefficient and v. Finally we study dynamics where the rotation of the tracer is limited by the presence of neighboring particles. We find that the effect of this rotational locking may be quantitatively described in terms of a reduction of the rotation rate.

Arrested states in persistent active matter: Gelation without attraction

“…In this limit, the self-propulsion directions of the particles are a "quenched" random variable, and we assign these uniformly with an equal number of the particles having an active direction along each of the four lattice directions. Since the cross shape leads to strong rotational locking [42], small finite D R leads to qualitatively similar results as the infinite persistence-time limit, including overall global arrest due to percolating gel-like structures, as shown in Appendix D.…”

“…The ASEP mechanism also provides a natural explanation for the length scales emerging in the morphology of the arrested states. By appealing to the dynamics of a single active tracer in a passive background of hard crosses [42], we showed that the dynamic differentiation between arrested and non-arrested states appears at times longer than that needed for the tracer dynamics to cross over from diffusive to ballistic. Thus, the gel-like arrest, in contrast to the glassy caging dynamics of the passive system is driven by activity.…”

“…We study a range of global densities between ρ = 0.10 and ρ = 0.17, and a range of activity values ∆v from 0 to 1. Note that even though ∆v is a dimensionless activity, it may take values larger than unity [42].The system domain is a two-dimensional square box of linear length L, periodic boundary conditions, and a fixed total number of particles N = ρL 2 . Unless otherwise stated, we present results for L = 450.…”

“…5 shows MSD and γ(t) measurements for individual runs at large and intermediate activity values, ∆v = 0.20 and ∆v = 0.07. We can construct a meanfield model for the behavior of γ(t) in the non-arrested states by using known results about the dynamics of a single non-rotating active tracer moving in a background of passive particles with density ρ [42]. For a non-rotating active tracer moving on a lattice at ρ = 0, the MSD is given by ∆r 2…”

Microscopic theory for the diffusion of an active particle in a crowded environment

“…The case of an active tracer in a dynamic environment has been the subject of only a few theoretical studies of particles evolving on a lattice (see however [40] for a very recent mode-coupling approach in continuous space), which focused mainly on the lowdensity limit of the problem, with a discrete-time description, with a tracer that never jumps sideways from the direction of propulsion, and with a specific dynamics [41]. Particular interactions between particles (third-neighbor exclusion) have also been studied through numerical simulations and mean-field approximations [42]. A generic analytical framework, that would allow the calculation of the diffusivity of an active tracer in a dynamic environ-ment for a wide range of parameters, and in particular for arbitrary density, is missing.…”