Aging Wiener-Khinchin Theorem

Physical Review Letters
N Leibovich, E Barkai

Abstract

The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms.

References

May 1, 1996·Physical Review. a·S MarksteinerP Zoller
Apr 12, 2003·Physical Review Letters·Eli Barkai
Jul 21, 2004·The Journal of Chemical Physics·G Margolin, E Barkai
Mar 5, 2009·Physical Review Letters·Ludovico SilvestriPaolo Allegrini
Aug 8, 2009·Physical Review Letters·Iddo Eliazar, Joseph Klafter
May 21, 2010·Physical Review Letters·Alessandro TaloniJoseph Klafter
Sep 28, 2010·Physical Review Letters·Gerardo AquinoBruce J West
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A DechantE Barkai
Oct 17, 2012·Physical Chemistry Chemical Physics : PCCP·Diego Krapf
Aug 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aljaž Godec, Ralf Metzler
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Leibovich, E Barkai
Mar 25, 2014·Physical Review Letters·Florin Ionita, Hildegard Meyer-Ortmanns
Apr 5, 2013·Physical Review Letters·Markus NiemannEli Barkai
Aug 30, 2014·Physical Review Letters·P L KrapivskyTridib Sadhu
Oct 4, 2014·Physical Review Letters·Chaitra HegdeAbhishek Dhar
Nov 7, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Miguel A Rodríguez
Sep 5, 2015·Physical Review Letters·Andreas Dechant, Eric Lutz

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Citations

Sep 5, 2015·Physical Review Letters·Andreas Dechant, Eric Lutz
Dec 15, 2016·Physical Review. E·N LeibovichE Barkai
Jul 16, 2017·Physical Review. E·Miguel A Rodríguez
Jan 20, 2018·Physical Review. E·N Leibovich, E Barkai
Aug 15, 2018·Optics Letters·Yen-Yin LiSheng-Lung Huang
Jun 24, 2020·The Journal of Chemical Physics·Somrita Ray, Shlomi Reuveni
Sep 28, 2017·Physical Review. E·Avinash Chand YadavDeepak Dhar

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