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

## TL;DR

This paper investigates the movement of an active tracer particle in a dense lattice gas with complex interactions, deriving analytical expressions and simulations to understand how activity and particle interactions influence tracer dynamics.

## Contribution

It provides new analytical formulas for tracer drift velocity and explores the effects of rotational diffusion and particle interactions on tracer motion.

## Key findings

- Analytical expression for tracer drift velocity v.
- Verification of theoretical results with numerical simulations.
- Rotational locking reduces the tracer's rotation rate.

## 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.