Conditional 1/fα noise: From single molecules to macroscopic measurement

N. Leibovich, E. Barkai

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number032132
JournalPhysical Review E
Issue number3
StatePublished - 19 Sep 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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