title: Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.
abstract: 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^{β} noise. Aging 1/f^{β} 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^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.
authors.affiliation: Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.
authors.forename: N
authors.initials: N
authors.lastname: Leibovich
authors.affiliation: Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.|Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Dechant
authors.affiliation: Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.
authors.forename: E
authors.initials: E
authors.lastname: Lutz
authors.affiliation: Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.
authors.forename: E
authors.initials: E
authors.lastname: Barkai