Optimal mean first-passage time of a run-and-tumble particle in a class of one-dimensional confining potentials

Abstract

We consider a run-and-tumble particle (RTP) in one dimension, subjected to a telegraphic noise with a constant rate γ, and in the presence of an external confining potential with . We compute the mean first-passage time (MFPT) at the origin for an RTP starting at x 0. We obtain a closed form expression for for all , which becomes fully explicit in the case and in the limit . For generic 1$ ?> we find that there exists an optimal rate that minimizes the MFPT and we characterize in detail its dependence on x 0. We find that as , while converges to a non-trivial constant as . In contrast, for p = 1, there is no finite optimum and in this case. These analytical results are confirmed by our numerical simulations.