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arXiv · 2310.00802

Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles

Manish Patel·Debasish Chaudhuri
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Abstract

In this study, we investigate the behavior of free inertial Active Brownian Particles (ABP) in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker-Planck equation is generally challenging, we utilize a Laplace transform method to obtain the exact temporal evolution of all dynamical moments in arbitrary dimensions. Our expressions in $d$ dimensions reveal that inertia significantly impacts steady-state kinetic temperature and swim pressure while leaving the late-time diffusivity unchanged. Notably, as a function of activity and inertia, the steady-state velocity distribution exhibits a remarkable re-entrant crossover from passive Gaussian to active non-Gaussian behaviors. We construct a corresponding phase diagram using the exact expression of the $d$-dimensional kurtosis. Our analytic expressions describe steady states and offer insights into time-dependent crossovers observed in moments of velocity and displacement. Our calculations can be extended to predict up to second-order moments for run-and-tumble particles (RTP) and the active Ornstein-Uhlenbeck process (AOUP). Additionally, the kurtosis shows differences from AOUP.

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Manish Patel, Debasish Chaudhuri. 2023-10-01. Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles. https://doi.org/10.1088/1367-2630/ad1538

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