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We derive equations of motion for the mean-squared displacement (MSD) of an active Brownian particle (ABP) in a crowded environment modeled by a dense system of passive Brownian particles, and of a passive tracer particle in a dense active-Brownian particle system, using a projection-operator scheme. The interaction of the tracer particle with the dense host environment gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for the glass transition in active Brownian particles (ABP-MCT), we discuss the various regimes of activity-induced super-diffusive motion and density-induced sub-diffusive motion. The predictions of the theory are shown to be in good agreement with results from an event-driven Brownian dynamics simulation scheme for the dynamics of two-dimensional active Brownian hard disks.
Self-propelled colloids constitute an important class of intrinsically non-equilibrium matter. Typically, such a particle moves ballistically at short times, but eventually changes its orientation, and displays random-walk behavior in the long-time l
Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically out-of-equilibrium
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S.
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels -- single-files, comb-like structures and quasi-one-dimensional channels with
In a microrheological set-up a single probe particle immersed in a complex fluid is exposed to a strong external force driving the system out of equilibrium. Here, we elaborate analytically the time-dependent response of a probe particle in a dilute