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Criticality and long-range correlations in time series in classical and quantum systems
E Landa1, Irving O Morales, R Fossion
1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México, DF, Mexico.
Summary
Transitional states between system regimes generate 1/f time series, indicating long-range correlations. This generic property applies to both classical and quantum systems, observed in logistic maps and nuclear spectra.
Area of Science:
- Complex Systems Science
- Statistical Physics
- Quantum Mechanics
Background:
- 1/f time series, also known as pink noise, exhibit power-law frequency spectra.
- These series are observed across diverse natural and artificial phenomena.
- Understanding the conditions for 1/f time series generation is crucial for characterizing complex systems.
Purpose of the Study:
- To investigate the occurrence of 1/f time series in transitional states between different system regimes.
- To demonstrate the generic nature of this phenomenon in both classical and quantum systems.
- To identify transitional points by their implied long-range correlations.
Main Methods:
- Analysis of the one-dimensional module-1 logistic map as a classical system example.
- Examination of nuclear excitation spectra from a schematic shell-model Hamiltonian as a quantum system example.
- Application of Fourier spectral analysis and detrended fluctuation analysis (DFA) to study system fluctuations.
Main Results:
- Transitional states between distinct regimes were found to imply the generation of 1/f time series.
- The 1/f time series property was observed to be generic, appearing in both classical and quantum systems studied.
- Long-range correlations, characteristic of 1/f time series, were identified as a key feature of transitional points.
Conclusions:
- The presence of 1/f time series is a robust indicator of transitional dynamics in complex systems.
- The findings suggest a unified mechanism for 1/f time series generation across different scientific domains.
- Further research can leverage these insights for analyzing and predicting behavior in systems exhibiting transitional states.
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