Criticality and long-range correlations in time series in classical and quantum systems

We present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1/f time series and that this property is generic in both classical and quantum systems. Our study focuses on two particular examples: the one-dimensional module-1 logistic map an...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 84; no. 1 Pt 2; p. 016224
Main Authors Landa, E, Morales, Irving O, Fossion, R, Stránský, P, Velázquez, V, Vieyra, J C López, Frank, A
Format Journal Article
LanguageEnglish
Published United States 01.07.2011
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Summary:We present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1/f time series and that this property is generic in both classical and quantum systems. Our study focuses on two particular examples: the one-dimensional module-1 logistic map and nuclear excitation spectra obtained with a schematic shell-model Hamiltonian. We suggest that a transitional point is characterized by the long-range correlations implied by 1/f time series. We apply a Fourier spectral analysis and the detrended fluctuation analysis method to study the fluctuations to each system.
ISSN:1550-2376
DOI:10.1103/PhysRevE.84.016224