Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers. (7th January 2022)

• Record Type: Journal Article
• Authors: Shee, Amir; Chaudhuri, Debasish
• Is Part Of: Journal of statistical mechanics. (2022:Jan.)
• Publication Date: 2022-01-07
• Subjects: active matter -- exact results -- stochastic particle dynamics -- Brownian motion; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac403f
• Languages: English
• ISSNs: 1742-5468

Abstract

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 several such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze the dynamical crossovers, determined by the orientational persistence of activity, speed fluctuation and relaxation. The kurtosis of displacement shows positive and negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed and orientational fluctuations, respectively.