Memory-enhanced diffusivity in stochastically forced walking droplets*

The motion of particles subject to random perturbations is a ubiquitous problem in numerous fields, including biology, active matter, and electronics. Whether induced by ambient fluctuations or spatial heterogeneities, the stochastic forces in these settings often lead the particle to exhibit diffusive behavior in the long-time limit. Recent experiments demonstrating the localization of walking droplets in disordered media have called into question the role that path memory, which is characterized by the wave-decay time in the walker system, may play in the emergent diffusive dynamics. We demonstrate that walking droplets subject to stochastic forces have straighter trajectories and thus an enhanced diffusion coefficient relative to active particles without path memory. Through an analysis of the nonlocal wave forces produced during a rapid change in the direction of the droplet, we find restoring forces that drive the walkers back to its past direction of motion, thereby rationalizing their memory-enhanced diffusion. Our results readily extend to similar systems with wave-dressed active particles and introduce the possibility to fine tune diffusion through variable memory.