Diffusion of passive tracer in an active bath

Active baths—ensembles of self-propelled entities such as bacteria, algae, or synthetic colloids—constitute a broad class of non-equilibrium systems capable of generating transport phenomena far beyond classical Brownian motion. Such environments are ubiquitous in biology—for instance, in intracellular cargo transport where passive tracers like vesicles navigate crowded cellular media agitated by molecular motors—and hold promise for engineering applications, such as targeted drug delivery in microfluidics or tunable rheology in active materials. Understanding how passive tracers move in these complex environments, particularly in the presence of transient interactions and structural disorder, is therefore essential for connecting microscopic activity to macroscopic transport properties, yet remains unexplored in models incorporating dynamic coupling. Here, we numerically investigate the transport properties of a passive tracer in a two-dimensional active bath composed of Active Ornstein-Uhlenbeck Particles (AOUPs), incorporating immobile obstacles and a novel transient harmonic coupling mechanism activated when the tracer-AOUP distance falls below a threshold TH. To this end, we analyze the mean squared displacement (MSD), time-dependent diffusivity, and probability density function (PDF) of the tracer’s displacement, exploring dependencies on parameters such as active particle density (θ_ac), spring stiffness (k), persistence time (τ), active noise strength (D_ac), and TH. Our findings reveal that, in obstacle-free environments, increasing tracer-active coupling and system size can give rise to enhanced diffusion and transient superdiffusive regimes driven by intermittent, collective tracer-active rearrangements. In contrast, the presence of immobile obstacles fundamentally alters this behavior, suppressing intermediate long-range transport and ultimately inducing subdiffusive or confined dynamics. Displacement PDFs exhibit persistent non-Gaussian features and approach stationary, bounded forms rather than converging to Gaussian statistics, reflecting nonequilibrium steady states shaped by active forcing, interaction-induced localization, and confinement. Together, these findings elucidate how dynamic coupling and environmental disorder jointly regulate nonequilibrium transport, with direct implications for intracellular dynamics and the design of synthetic active systems.