A run-and-tumble particle around a spherical obstacle: the steady-state distribution far-from-equilibrium

We investigate the steady-state distribution function of a run-and-tumble particle (RTP) evolving around a repulsive hard spherical obstacle. We demonstrate that the well-documented activity-induced attraction translates into a delta-peak accumulation at the obstacle's surface accompanied by an algebraic divergence of the density profile close to the obstacle. We obtain the full form of the distribution function in the regime where the typical distance run by the particle between two consecutive tumbles is much larger than the obstacle's size. This finding provides an expression for the low-density pair distribution function of a fluid of highly persistent hard-core RTP. It also advances an expression for the steady-state probability distribution of highly ballistic active Brownian particles and active Ornstein-Uhlenbeck particles around hard spherical obstacles.