Active Brownian particle under stochastic position and orientation resetting in a harmonic trap

TL;DR

This paper provides an exact analytical study of an Active Brownian Particle with stochastic position and orientation resetting in a harmonic trap, revealing rich dynamical behaviors and phase diagrams.

Contribution

It introduces a Fokker-Planck renewal approach to derive exact moments and analyze non-Gaussian behavior in a resetting active particle system.

Findings

Identified Gaussian and non-Gaussian regimes based on excess kurtosis.

Derived exact moments including mean displacement and MSD.

Mapped steady-state phase diagrams with respect to activity, resetting rate, and trap strength.

Abstract

We present an exact analytical study of an Active Brownian Particle (ABP) subject to both position and orientation stochastic resetting in a two-dimensional harmonic trap. Utilizing a Fokker-Planck-based renewal approach, we derive the system's exact moments, including the mean parallel displacement, mean squared displacement (MSD), and the fourth-order moment of displacement, and compare these with numerical simulations. To capture deviations from Gaussian behavior, we analyze the excess kurtosis, which reveals rich dynamical crossovers over time. These transitions span from Gaussian behavior (zero excess kurtosis) to two distinct non-Gaussian regimes: an activity-dominated regime (negative excess kurtosis) and a resetting-dominated regime (positive excess kurtosis). Furthermore, we quantify the steady-state phase diagrams by varying three key control parameters: activity, resetting rate, and harmonic trap strength, using steady-state excess kurtosis as the primary metric.