Run and tumble particle under resetting: a renewal approach

TL;DR

This paper analyzes a run and tumble particle with stochastic velocity reversals under Poissonian resetting, revealing that the stationary state is independent of velocity resetting, but absorption times depend on the resetting protocol.

Contribution

It introduces a renewal approach to study run and tumble particles with resetting, showing the stationary state is unaffected by velocity protocol while absorption times vary.

Findings

Stationary state independent of velocity resetting protocol.

Mean time to absorption is shorter with velocity randomization.

Renewal equation approach effectively analyzes resetting effects.

Abstract

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.