# Intermediate scattering function of an anisotropic active Brownian particle

## TL;DR

This paper derives exact analytical expressions for the intermediate scattering function of an anisotropic active Brownian particle, revealing how stochastic fluctuations and directed motion influence its spatio-temporal behavior.

## Contribution

It provides the first exact analytical formulas for the intermediate scattering function of a 3D anisotropic active Brownian particle, linking microscopic motion to measurable scattering data.

## Key findings

- Oscillatory behavior at intermediate wavenumbers indicates persistent swimming.
- Different temporal regimes show effective diffusion and directed motion.
- Results serve as a reference for experimental and more complex models.

## Abstract

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.