The power spectrum of a stationary process is calculated using the Wiener-Khinchin theorem which gives the connection between the power spectrum and the correlation function of the observed process [1,2]. Recently, the power spectrum of intermittent quantum dots was measured showing that the power spectrum ages as the measurement time is increased, indicating a non-stationary behavior [3]. In the talk I present the generalized Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum <S_tm(ω)> where t_m is the measurement time. Further, for processes with an aging autocorrelation function of the form <I(t)I(t+\tau)>=t^ΥΦ_EA(τ/t), where Φ_EA(x) is a nonanalytic function when x is small, an aging 1/f^β noise is found [4-6]. Aging 1/f^β noise is characterized by five critical exponents which are related to the scaled autocorrelation function. In addition I discuss the apparent infrared divergence of 1/f^β noise, where in a bounded process the 1/f^β spectrum must depends on the measurement time [6].  We illustrate our results for blinking-quantum-dot models, single-file diffusion and Brownian motion in a logarithmic potential.

[1] R.Kubo, M.Toda, and H. Hashitsume, Statistical Physics II- Nonequilibrium Statistical Mechanics, (Springer, Berlin, 1995).

[2] M. B. Priestley, Spectral Analysis and Time Series, (Academic, London, 1981).

[3] S. Sadegh, E. Barkai and D. Krapf, Five critical exponents describing 1/f noise for intermittent quantum dots, New J. Phys. 16, 113054 (2014).

[4] N. Leibovich and E. Barkai, Aging Wiener-Khinchin Theorem, Phys. Rev. Lett. 115, 080602 (2015).

[5] A. Dechant and E. Lutz, Wiener-Khinchin theorem for nonstationary scale-invariant processes, Phys. Rev. Lett. 115, 080603 (2015).

[6] N. Leibovich, A. Dechant, E. Lutz and E. Barkai, Aging Wiener-Khinchin Theorem and Critical Exponents of 1/f^β Noise, arXiv:1603.05440v1 (2016).