Contrasting Effects of Memory on Enhanced Diffusion in Active Matter

Ubiquitous in noisy active matter, enhanced diffusion is the result of persistent orientation of the velocity.  Here, we discuss two active systems with path memory influencing the motion that exhibit different effects on the enhanced diffusion.  The first is a swimming droplet that leaves behind a chemical concentration trail, governed by a heat-like equation. The second is a bouncing droplet that produces a trailing wave-field. In the former, memory causes self-trapping that reduces the enhanced diffusion, while in the latter, memory produces a restoring force normal to the trajectory that increases the enhanced diffusion by increasing the persistence of the orientation of the velocity.  These systems illustrate the complex interplay between memory and noise in active matter.