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

N Leibovich¹, E Barkai¹

¹Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel.

Physical Review. E

|January 20, 2018

Summary

Single-molecule noise measurements reveal 1/f^{α} noise is nonstationary, unlike bulk measurements. This difference arises from the increasing number of fluctuating units over time, obscuring the true dynamics in macroscopic observations.

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Area of Science:

Physics
Physical Chemistry
Nanotechnology

Background:

Macroscopic measurements of 1/f^{α} noise often assume stationarity.
Single-molecule and nano-object dynamics can exhibit complex, time-dependent behavior.

Purpose of the Study:

To investigate the distinct characteristics of 1/f^{α} noise at the single-particle level compared to macroscopic measurements.
To elucidate the reasons behind the apparent stationarity observed in bulk measurements.

Main Methods:

Analysis of single-molecule and nano-object noise measurements.
Utilizing stochastic and deterministic models, including superimposed Lorentzians and blinking quantum dot models.
Exploring deterministic dynamics via nonlinear mapping.

Main Results:

Single-particle measurements of 1/f^{α} noise yield conditional time-dependent spectra.
Macroscopic measurements appear stationary due to an increasing number of fluctuating units over experimental timescales.
The inherent non-stationarity of 1/f^{α} spectra is masked in bulk measurements.

Conclusions:

1/f^{α} noise at the single-particle level is fundamentally nonstationary.
Macroscopic averaging conceals the underlying time-dependent nature of single-unit fluctuations.
Understanding single-particle dynamics is crucial for interpreting complex noise phenomena.