TY - JOUR
T1 - Aging Wiener-Khinchin Theorem
AU - Leibovich, N.
AU - Barkai, E.
N1 - Publisher Copyright:
© 2015 American Physical Society. © 2015 American Physical Society.
PY - 2015/8/21
Y1 - 2015/8/21
N2 - The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function (t)I(t+τ). We consider nonstationary processes with the widely observed aging correlation function I(t)I(t+τ)∼tγφEA(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 φEA(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.
AB - The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function (t)I(t+τ). We consider nonstationary processes with the widely observed aging correlation function I(t)I(t+τ)∼tγφEA(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 φEA(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.
UR - http://www.scopus.com/inward/record.url?scp=84940676074&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.115.080602
DO - 10.1103/PhysRevLett.115.080602
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C2 - 26340172
AN - SCOPUS:84940676074
SN - 0031-9007
VL - 115
JO - Physical Review Letters
JF - Physical Review Letters
IS - 8
M1 - 080602
ER -