Abstract
We demonstrate that the measurement of 1/fα 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/fα spectrum is inherently nonstationary even if the macroscopic measurement completely obscures the underlying time dependence of the phenomena.
Original language | English |
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Article number | 032132 |
Journal | Physical Review E |
Volume | 96 |
Issue number | 3 |
DOIs | |
State | Published - 19 Sep 2017 |
Bibliographical note
Publisher Copyright:© 2017 American Physical Society.
Funding
We thank the Israel Science Foundation for funding.
Funders | Funder number |
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Israel Science Foundation |