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Gómez, J. M. G. and Faleiro, E. and Molina, R. A. and Muñoz, L. and Relaño Pérez, Armando
(2005)
*Chaos and 1/f noise in nuclear spectra.*
In
Key Topics in Nuclear Structure: Proceedings of the 8th International Spring Seminar on Nuclear Physics Paestum, Italy, 23 – 27 May 2004.
World Scientific Publishing Company, pp. 577-584.
ISBN 978-981-256-093-3

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Official URL: http://dx.doi.org/10.1142/9789812702265_0063

## Abstract

Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum S(f) which is a power function of the frequency f . Examples with this behavior are the Sun spot activity, the human heartbeat, the DNA sequence, or Bach’s First Brandenburg Concert. In this work, we show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series, with energy playing the role of time. Because of this analogy, the fluctuations of quantum energy spectra can be studied using traditional methods of time series, like calculating the Fourier transform and studying the power spectrum. We present the results for paradigmatic quantum chaotic systems like atomic nuclei (by means of large scale shell-model calculations) and the predictions of random matrix theory. We have found a surprising general property of quantum systems: The energy spectra of chaotic quantum systems are characterized by 1= f noise, while regular quantum systems exhibit 1= f^2 noise. Some other interesting applications of this time series analogy are a test of the existence of quantum chaos remnants in the nuclear masses, and the study of the order to chaos transition in semiclassical systems. In this case, it is found that the energy level spectrum exhibits 1= f^α noise with the exponent changing smoothly from α = 2 in regular systems to α= 1 in chaotic systems.

Item Type: | Book Section |
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Additional Information: | © 2005 World Scientific Publishing Company. |

Uncontrolled Keywords: | Quantum chaos; Nuclei; Time series |

Subjects: | Sciences > Physics |

ID Code: | 35529 |

Deposited On: | 04 Feb 2016 15:18 |

Last Modified: | 04 Feb 2016 15:18 |

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