1/f noise and low-frequency cutoff paradox

Starting with the work of Bernamont (1937) on resistance uctuations, noisy signals of a vast number of natural processes exhibit 1/f power-spectrum. This power spectrum is non-integrable implying that the total energy in the system is infnite. As pointed out by Mandelbrot (1950's) this infrared catastrophe suggests that one should abandon the stationary mind set and hence go beyond the widely applicable Wiener-Khinchin formula for the power spectrum. Recent theoretical and experimental advances renewed the discussion on this old paradox, for example in the context of blinking quantum dots [1,2]. In this talk aging, intermittency, ergodicity breaking, and critical exponents of the sample power spectrum are discussed within a theoretical framework which hopefully provides new insight on the 1/f enigma [3].

[1] M. Niemann, H. Kantz, E. Barkai, Fluctuations of 1/f noise and the low frequency cutoff paradox, Phys. Rev. Lett. 110, 140603 (2013).
[2] S. Sadegh, E. Barkai, and D. Krapf, 1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents, New. J. of Physics 16 (2014)
113054.
[3] N. Leibovich and E. Barkai, Aging Wiener-Khinchin Theorem, Phys. Rev. Lett. 115, 080602 (2015).