2012/09/10 by Markus Niemann, Holger Kantz, Hölger Kantz +1 · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Computer science #Connection (principal bundle) #Cutoff #Ergodicity #Geometry #Intermittency #Mathematics #Noise (video) #Parseval's theorem #Physics #Power law #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #Turbulence #cond-mat.stat-mech #physics.data-an #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.110.140603
5 pages, 2 figures, supplementary material (4 pages)
arxiv created 2012/09/10 · openalex publication_date 2013/04/02 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recent experiments on blinking quantum dots, weak turbulence in liquid crystals, and nanoelectrodes reveal the fundamental connection between 1/f noise and power law intermittency. The nonstationarity of the process implies that the power spectrum is random--a manifestation of weak ergodicity breaking. Here, we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve in this case an outstanding paradox on the nonintegrability of 1/f noise and the violation of Parseval's theorem. We explain why there is no physical low-frequency cutoff and therefore why it cannot be found in experiments.