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

¹ Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 4 Place Jussieu, 75252 Paris Cedex 05, France
² LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay - 91405 Orsay, France

Received: 17 November 2023
Accepted: 21 February 2024

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 x₀. We obtain a closed form expression for for all , which becomes fully explicit in the case and in the limit . For generic we find that there exists an optimal rate that minimizes the MFPT and we characterize in detail its dependence on x₀. 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.