Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

Abstract

We investigate the stochastic behavior of the single-trajectory spectral density $S(\omega ,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $\omega$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(\omega ,\mathcal{T})$ for different values of $\omega$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

arXiv comment29 pages, 7 figures

References in corpus (34)

• Review of the Low-Frequency 1/f Noise in Graphene Devices
• Quantifying dissipation using fluctuating currents
• On the heat flux and entropy produced by thermal fluctuations
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Spectral content of a single non-Brownian trajectory
• Non-equilibrium and information: the role of cross-correlations
• Experimental Realization of a Minimal Microscopic Heat Engine
• 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
• Two-temperature Langevin dynamics in a parabolic potential
• Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations
• Aging Wiener-Khinchin Theorem
• Spectral content of fractional Brownian motion with stochastic reset
• 1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents
• Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise
• Single-trajectory spectral analysis of scaled Brownian motion
• Universal spectral features of different classes of random diffusivity processes
• Aging power spectrum of membrane protein transport and other subordinated random walks
• Two-temperature Brownian dynamics of a particle in a confining potential
• Asymmetry relations and effective temperatures for biased Brownian gyrators
• Temporal correlations of the running maximum of a Brownian trajectory
• The Power Spectrum of Ionic Nanopore Currents: The Role of Ion Correlations
• A simple system with two temperatures
• An autonomous out of equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
• Non-equilibrium probability flux of a thermally driven micromachine
• Information-theoretic analysis of the directional influence between cellular processes
• Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator
• Spectral density of individual trajectories of an active Brownian particle
• Tracer Diffusion on a Crowded Random Manhattan Lattice
• Fraudulent White Noise: Flat power spectra belie arbitrarily complex processes
• Current-mediated synchronization of a pair of beating non-identical flagella
• Passive advection of fractional Brownian motion by random layered flows
• Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

Cited by in corpus (2)

• Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator
• Fractional Brownian Gyrator