Erratum: Aging Wiener-Khinchin theorem and critical exponents of 1/f

This corrects the article DOI: 10.1103/PhysRevE.94.052130.

Aging Wiener-Khinchin theorem and critical exponents of 1/f

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{ß} noise. Aging 1/f^{ß} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{ß} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials.

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Fluctuations of time averages for Langevin dynamics in a binding force field.

We derive a simple formula for the fluctuations of the time average x(t) around the thermal mean (eq) for overdamped brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.

Generation of 0.4-keV femtosecond electron pulses using impulsively excited surface plasmons.

We demonstrate the generation of 0.4-keV, sub-27 fs electron pulses using low-intensity laser pulses from a Ti:sapphire oscillator through the excitation of surface plasmon waves on a time scale within the plasmon lifetime. Modeling of the ponderomotive electron pulse acceleration yields electron energy spectra that are in excellent agreement with the observed ones. Our work opens a doorway for time-resolved experimentation using low-power, high-repetition rate laser pulses.