Condensed Matter Seminar: 1/f noise and the low frequecy cutoff paradox

Abstract:

Starting with the work of Bernamont (1937) on resistance uctuations, noisy signals of a vast number of natural processes exhibit 1=f power-spectrum. Such spectra are found in weather data, brain activity, currents of ion-channels and certain chaotic systems to name a few. The wide applicability of this spectrum resulted in conicting theories distributed among many disciplines.

A unifying feature is that 1=f power spectrum is non-integrable at low frequencies implying that the total energy in the system is in nite, i.e. the spectral desnity is not normalizable. 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 appli-cable Wiener-Khinchin theorem for the power spectrum. Recent theoretical and experi-mental advances renewed the discussion on this old paradox, for example in the context of blinking quantum dots [1,2]. Importantly the removal of ensemble averaging in nano-scale measurement revealed time dependent spectrum, at least for nano-crystals.

In this talk ageing, intermittency, weak ergodicity breaking, and critical exponents of the sample power spectrum are discussed within a theoretical framework which hopefully provides new insights on the 1=f enigma [1,3]. A general theoretical framework based on non stationary but scale invariant correlation functions leads to an ageing Wiener-Khinchin theorem which replaces the standard spectral theory [3]. The non-integrable spectral density is reminiscent of the in nite invariant measure found in in nite ergodic theory.

References:

[1] M. Niemann, H. Kantz, E. Barkai Fluctuations of 1/f noise and the low frequency cuto paradox Phys. Rev. Lett. 110, 140603 (2013). M. Niemann, E. Barkai, and H. Kantz Renewal theory for a system with internal states Mathematical Modelling of Natural Phenomena (special issue on anomalous di usion) 11 3 (2016) 191-239.

[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 113054 (2014).

[3] N. Leibovich and E. Barkai, Aging Wiener-Khinchin Theorem Phys. Rev. Lett. 115, 080602 (2015). N. Leibovich, A. Dechant, E. Lutz, and E. Barkai Aging Wiener-Khinchin theorem and critical exponents of 1=f noise Phys. Rev. E. 94, 052130 (2016).

Event Organizer: Prof. Eli Eisenberg