Universal transport of active colloids with sensory delay in motility landscapes
We experimentally, numerically and analytically explore the diffusive transport of active colloidal particles with sensory delay, navigating motility landscapes in which the self-propulsion speed depends on space. We show how the transport properties can be obtained by replacing the space dependence of the self-propulsion speed by a dynamical stochastic switching process in the absence of delay, and extend the theory for systems with finite delayed responses. We obtain analytical results for the mean square displacement and the effective diffusion coefficient which accurately predict experimental measurements and numerical simulations across multiple scales. We show how, within the regime of validity of the delay-extended theory, density patterns and effective diffusion obey universal scaling forms. Our work provides minimal framework describing the transport properties of active swimmers with internal adaptation dynamics in motility landscapes.