Spectral density of individual trajectories of an active Brownian particle

Abstract

We study analytically the single-trajectory spectral density (STSD) of an active Brownian motion as exhibited, for example, by the dynamics of a chemically-active Janus colloid. We evaluate the standardly-defined spectral density, i.e. the STSD averaged over a statistical ensemble of trajectories in the limit of an infinitely long observation time $T$, and also go beyond the standard analysis by considering the coefficient of variation $\gamma$ of the distribution of the STSD. Moreover, we analyse the finite-$T$ behaviour of the STSD and $\gamma$, determine the cross-correlations between spatial components of the STSD, and address the effects of translational diffusion on the functional forms of spectral densities. The exact expressions that we obtain unveil many distinctive features of active Brownian motion compared to its passive counterpart, which allow to distinguish between these two classes based solely on the spectral content of individual trajectories.

21 pages, 7 figures

References in corpus (15)

• Self-motile colloidal particles: from directed propulsion to random walk
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Motility-Induced Phase Separation
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• A self-propelled particle in an external potential: is there an effective temperature?
• Spectral content of a single non-Brownian trajectory
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Intermediate scattering function of an anisotropic active Brownian particle
• First-passage time of run-and-tumble particles
• Aging power spectrum of membrane protein transport and other subordinated random walks
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
• Local time for run and tumble particle
• Large fluctuations of the area under a constrained Brownian excursion
• Clogging, Dynamics and Reentrant Fluid for Active Matter on Periodic Substrates
• Dry, aligning, dilute, active matter: A synthetic and self-contained overview

Cited by in corpus (7)

• Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator
• Chiral run-and-tumble walker: transport and optimizing search
• Diffusion coefficient and power spectrum of active particles with a microscopically reversible mechanism of self-propelling
• Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
• Active colloid with externally induced periodic bipolar motility and its cooperative motion
• Long time behavior of run-and-tumble particles in two dimensions
• Universal framework for the long-time position distribution of free active particles