Fluctuations of $1/f$ noise and the low frequency cutoff paradox

Abstract

Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is random -- a manifestation of weak ergodicity breaking. Here we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve an outstanding paradox on the non integrability of $1/f$ noise and the violation of Parseval's theorem. We explain why there is no physical low frequency cutoff and therefore cannot be found in experiments.

5 pages, 2 figures, supplementary material (4 pages)

References in corpus (6)

• Universal emission intermittency in quantum dots, nanorods, and nanowires
• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Weakly non-ergodic Statistical Physics
• Nonergodisity of a time series obeying Lévy statistics
• A random telegraph signal of Mittag-Leffler type

Cited by in corpus (47)

• Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution
• Spectral content of a single non-Brownian trajectory
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Environmental noise spectroscopy with qubits subjected to dynamical decoupling
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Aging Wiener-Khinchin Theorem
• 1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents
• 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
• Wiener-Khinchin theorem for nonstationary scale-invariant processes
• Modeling and Analysis of SiNW FET-Based Molecular Communication Receiver
• Optimization and universality of Brownian search in quenched heterogeneous media
• Efficiency of tidal dissipation in slowly rotating fully convective stars or planets
• Fast shuttling of a particle under weak spring-constant noise of the moving trap
• Modeling and Analysis of SiNW BioFET as Molecular Antenna for Bio-Cyber Interfaces towards the Internet of Bio-NanoThings
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
• An intrinsic pink-noise multi-decadal global climate dynamics mode
• 1/f noise and long-term memory of coherent structures in a turbulent shear flow
• Impact of correlations and heavy-tails on quantum error correction
• Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator
• Spectral density of individual trajectories of an active Brownian particle
• A general mechanism for the `$1/f$' noise
• Quantum flicker noise in atomic and molecular junctions
• $1/f^{\alpha }$ power spectrum in the Kardar-Parisi-Zhang universality class
• Conditional $1/f^{\alpha }$ noise: from single molecules to macroscopic measurements
• 1/f Noise from the Laws of Thermodynamics for Finite-Size Fluctuations
• $1/f^{\beta }$ noise for scale-invariant processes: How long you wait matters
• Dynamics of switching processes: general results and applications to intermittent active motion
• $1/f$ noise from the sequence of nonoverlapping rectangular pulses
• Exact decoherence dynamics of $1/f$ noise
• Passive advection of fractional Brownian motion by random layered flows
• Measurement-induced cooling of a qubit in structured environments
• Apparent universality of $1/f$ spectra as an artifact of finite-size effects
• $1/f$ noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers
• Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
• Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes
• Deconstructing $1/f$ noise and its universal crossover to non-$1/f$ behavior
• Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence
• Nonlinear deterministic-chaotic collapse model -- preliminaries, philosophy, locality
• Classification of anomalous diffusion in animal movement data using power spectral analysis
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations
• Immediate recapture in the trapping-detrapping process of a single charge carrier
• On the Capacity of Diffusion-Based Molecular Communications with SiNW FET-Based Receiver
• Estimating relaxation times from a single trajectory
• Scaling theory for the $1/f$ noise
• Two-dimensional fractional Brownian motion: Analysis in time and frequency domains