Run-and-Tumble particles in Two-dimensions under Stochastic Resetting

TL;DR

This paper investigates how stochastic resetting influences a two-dimensional run-and-tumble particle, analyzing stationary distributions, relaxation dynamics, and first passage times, revealing how resetting can optimize search efficiency.

Contribution

It introduces a comprehensive analysis of positional and orientational resetting effects on RTPs, including stationary states, relaxation behavior, and first passage properties, which were not previously explored.

Findings

Radial distribution approaches a constant near the origin.

X-marginal distribution diverges logarithmically at zero.

Resetting can minimize mean first passage time.

Abstract

We study the effect of stochastic resetting on a run and tumble particle (RTP) in two spatial dimensions. We consider a resetting protocol which affects both the position and orientation of the RTP: with a constant rate the particle undergoes a positional resetting to a fixed point in space and orientation randomization. We compute the radial and $x$-marginal stationary state distributions and show that while the former approaches a constant value as $r \to 0$, the latter diverges logarithmically as $x \to 0$. On the other hand, both the marginal distributions decay exponentially with the same exponent far away from the origin. We also study the temporal relaxation of the RTP and show that the position distribution undergoes a dynamical transition to a stationary state. We also study the first passage properties of the RTP in the presence of the resetting and show that the optimization of the resetting rate can minimize the mean first passage time. We also give a brief discussion on the stationary states for resetting to the initial position with fixed orientation.