# Diffusion, subdiffusion and localisation of active colloids in random post lattices

## TL;DR

This study combines experiments and theory to explore how active colloids move in crowded environments, revealing a transition from diffusion to localization driven by obstacle density and interactions, with critical behavior at the percolation threshold.

## Contribution

It provides a detailed analysis of the transition mechanisms of active colloids in random lattices, highlighting the roles of different interactions and identifying the critical conditions for localization.

## Key findings

- Colloids transition from diffusive to localized with increasing obstacle density.
- Repulsion and hard-core interactions slow down long-time diffusion.
- Localization occurs at the void-percolation threshold, with subdiffusion at critical density.

## Abstract

Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive, to subdiffusive, to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids. In contrast, the localization transition stems solely from excluded-volume interactions and occurs at the void-percolation threshold. Within this critical scenario, equivalent to that of the random Lorentz gas, genuine asymptotic subdiffusion is found only at the critical density where the motile particles explore a fractal maze.