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Aging Wiener-Khinchin Theorem.

N Leibovich1, E Barkai1

  • 1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.

Physical Review Letters
|September 5, 2015
PubMed
Summary

This study extends the Wiener-Khinchin theorem to analyze nonstationary random signals with aging correlations. It introduces two new theorems linking power spectra to correlation functions, revealing 1/f-type spectra from nonanalytical scaling functions.

Area of Science:

  • Statistical physics
  • Signal processing
  • Complex systems

Background:

  • The Wiener-Khinchin theorem connects the power spectrum and correlation function for stationary random signals.
  • Nonstationary processes with aging correlations are common in nature but less understood theoretically.
  • Existing methods struggle to analyze the spectral properties of these complex systems.

Purpose of the Study:

  • To generalize the Wiener-Khinchin theorem for nonstationary processes with aging correlations.
  • To establish a theoretical framework for relating power spectra to correlation functions in aging systems.
  • To identify conditions leading to 1/f-type spectra in these systems.

Main Methods:

  • Formulation of two novel aging Wiener-Khinchin theorems.

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  • Analysis of the relationship between power spectrum and time/ensemble-averaged correlation functions.
  • Investigation of scaling functions exhibiting nonanalytical behavior.

    • Main Results:

    • Two aging Wiener-Khinchin theorems are proposed, offering different analytical advantages.
    • Nonanalytical behavior in the scaling function predicts aging 1/f-type spectra.
    • The framework is validated using examples like blinking quantum dots and diffusion processes.

    Conclusions:

    • The developed aging Wiener-Khinchin theorems provide a powerful tool for analyzing nonstationary signals.
    • The study clarifies the origin of 1/f-type spectra in various physical systems.
    • The approach demonstrates broad applicability across diverse scientific mechanisms.