Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

TL;DR

This paper provides an exact analytical framework for understanding the dynamics of active Brownian particles with fluctuating speeds in arbitrary dimensions, revealing complex crossover behaviors and deviations from Gaussian displacement distributions.

Contribution

It introduces a Laplace transform-based method to exactly compute dynamical moments for active particles with speed fluctuations, extending analysis to arbitrary dimensions.

Findings

Explicit moments for active Brownian motion with speed fluctuations

Identification of dynamical crossovers in particle behavior

Displacement kurtosis varies with fluctuation dominance

Abstract

We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein-Uhlenbeck process for active speed generation. Using a Laplace transform approach, we describe and use a Fokker-Planck equation-based method to evaluate the exact time dependence of all relevant dynamical moments. We present explicit calculations of such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze several dynamical crossovers. The kurtosis of displacement shows positive or negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed or orientational fluctuations.