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Conditional 1/f^{α} noise: From single molecules to macroscopic measurement.

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We demonstrate that the measurement of 1/f^{α} noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single-particle measurements yield… Click to show full abstract

We demonstrate that the measurement of 1/f^{α} noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single-particle measurements yield a conditional time-dependent spectrum. However, the number of units fluctuating on the time scale of the experiment is increasing in such a way that the macroscopic measurements appear perfectly stationary. The single-particle power spectrum is a conditional spectrum, in the sense that we must make a distinction between idler and nonidler units on the time scale of the experiment. We demonstrate our results based on stochastic and deterministic models, in particular the well-known approach of superimposed Lorentzians, the blinking quantum dot model, and deterministic dynamics generated by a nonlinear mapping. Our results show that the 1/f^{α} spectrum is inherently nonstationary even if the macroscopic measurement completely obscures the underlying time dependence of the phenomena.

Keywords: macroscopic measurement; conditional noise; time; noise single

Journal Title: Physical Review E
Year Published: 2017

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