Survival probability and position distribution of a run and tumble particle in U(x) = α|x| potential with an absorbing boundary

Abstract

We study the late-time exponential decay of the survival probability [ image ], of a one-dimensional run-and-tumble particle starting from [ image ] with an initial orientation [ image ], under a confining potential [ image ] with an absorbing boundary at [ image ]. We find that the decay rate [ image ] of the survival probability has a strong dependence on the location a of the absorbing boundary, which undergoes a freezing transition at a critical value [ image ], where [ image ] is the self-propulsion speed and γ is the tumbling rate of the particle. For [ image ], the value of [ image ] increases monotonically from zero, as a decreases from infinity, until it attains the maximum value [ image ] at [ image ]. For [ image ], the value of [ image ] freezes to the value [ image ]. We also obtain the propagator with the absorbing boundary condition at x = a. Our analytical results are supported by numerical simulations.