Wiener-Khinchin Theorem for Nonstationary Scale-Invariant Processes

Physical Review Letters
Andreas Dechant, E Lutz

Abstract

We derive a generalization of the Wiener-Khinchin theorem for nonstationary processes by introducing a time-dependent spectral density that is related to the time-averaged power. We use the nonstationary theorem to investigate aging processes with asymptotically scale-invariant correlation functions. As an application, we analyze the power spectrum of three paradigmatic models of anomalous diffusion: scaled Brownian motion, fractional Brownian motion, and diffusion in a logarithmic potential. We moreover elucidate how the nonstationarity of generic subdiffusive processes is related to the infrared catastrophe of 1/f noise.

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Citations

Sep 5, 2015·Physical Review Letters·N Leibovich, E Barkai
Jan 20, 2018·Physical Review. E·N Leibovich, E Barkai
May 31, 2019·Nature Communications·Eveline RigoGregory Timp
Dec 15, 2016·Physical Review. E·N LeibovichE Barkai

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