Survival probability and position distribution of a run and tumble particle in U ( x ) ...

Abstract

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