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.

arXiv comment21 pages, 7 figures

References in corpus (52)

• Active Particles in Complex and Crowded Environments
• 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
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Swimming in circles: Motion of bacteria near solid boundaries
• How far from equilibrium is active matter?
• Sedimentation of active colloidal suspensions
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Pressure is not a state function for generic active fluids
• The 2019 Motile Active Matter Roadmap
• Active Brownian Motion Tunable by Light
• Brownian motion of a self-propelled particle
• A self-propelled particle in an external potential: is there an effective temperature?
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Active Brownian Motion in Two Dimensions
• 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
• Fluctuations of $1/f$ noise and the low frequency cutoff paradox
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Run-and-tumble particles in two-dimensions : Marginal position distributions
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments
• Properties of additive functionals of Brownian motion with resetting
• Aging Wiener-Khinchin Theorem
• Spectral content of fractional Brownian motion with stochastic reset
• Active colloids in the context of chemical kinetics
• Active Brownian Motion with Directional Reversals
• Diffusion properties of active particles with directional reversal
• Sedimentation of self-propelled Janus colloids: polarization and pressure
• Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise
• Aging power spectrum of membrane protein transport and other subordinated random walks
• Single-trajectory spectral analysis of scaled Brownian motion
• Universal spectral features of different classes of random diffusivity processes
• Temporal correlations of the running maximum of a Brownian trajectory
• The Airy distribution: experiment, large deviations and additional statistics
• Active Brownian particles: mapping to equilibrium polymers and exact computation of moments
• Toward the full short-time statistics of an active Brownian particle on the plane
• Local time for run and tumble particle
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
• Clogging, Dynamics and Reentrant Fluid for Active Matter on Periodic Substrates
• Large fluctuations of the area under a constrained Brownian excursion
• Tracer Diffusion on a Crowded Random Manhattan Lattice
• Area fluctuations on a subinterval of Brownian excursion
• Passive advection of fractional Brownian motion by random layered flows
• 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