Publication:
Chaos and 1/f noise in nuclear spectra

dc.book.titleKey Topics in Nuclear Structure: Proceedings of the 8th International Spring Seminar on Nuclear Physics Paestum, Italy, 23 – 27 May 2004
dc.contributor.authorGómez, J. M. G.
dc.contributor.authorFaleiro, E.
dc.contributor.authorMolina, R. A.
dc.contributor.authorMuñoz, L.
dc.contributor.authorRelaño Pérez, Armando
dc.contributor.editorCovello, Aldo
dc.date.accessioned2023-06-20T13:43:07Z
dc.date.available2023-06-20T13:43:07Z
dc.date.issued2005-03
dc.description© 2005 World Scientific Publishing Company. International Spring Seminar on Nuclear Physics (8º. 2004. Paestum (Italia). This work is supported in part by Spanish Government grants BFM2003-04147-C02 and FTN2003-08337-C04-04.
dc.description.abstractMany 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.
dc.description.departmentDepto. de Estructura de la Materia, Física Térmica y Electrónica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipGobierno de España
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/35529
dc.identifier.citation1. B. B. Mandelbrot, Multifractals and 1/f noise (Springer, New York, 1999). 2. M. Schroeder, Fractals, Chaos and Power Laws (Freeman, New York, 1992). 3. H. J. Stöckmann, Quantum Chaos, (Cambridge University Press, Cambridge, 1999). 4. A. Relaño, J. M. G. Gómez, R. A. Molina, J. Retamosa and E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002). 5. M. L. Mehta, Random Matrices, (Academic Press, 1991) 6. E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, J. Retamosa, and A. P. Zuker, Phys. Rev. C 59, 2033 (1999). 7. B. H. Wildenthal, in Progress in Particle and Nuclear Physics, Ed. D. H. Wilkinson, Vol. 11 (Pergamon, Oxford 1984). 8. E. Caurier, F. Nowacki, A. Poves, and J. Retamosa, Phys. Rev. C 58, 2033 (1998). 9. E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño and J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004). 10. O. Bohigas, P. Leboeuf, Phys. Rev. Lett. 88, 92502 (2002). 11. J. Barea, A. Frank, J. G. Hirsch, and P. V. Isacker, Phys. Rev. Lett 95, 102501 (2005). 12. P. Möller, J. R. Nix, W. D. Myers, W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 13. J. Duflo and A. P. Zuker, Phys. Rev. C 52, R23 (1995). 14. J. M. G. Gómez, A. Relaño, J. Retamosa, E. Faleiro, L. Salasnich, M. Vranicar, and M. Robnik, Phys. Rev. Lett. 94, 084101 (2005). 15. M. S. Santhanam and J. N. Bandyopadhyay, Phys. Rev. Lett. 95, 114101 (2005).
dc.identifier.doi10.1142/9789812702265_0063
dc.identifier.isbn978-981-256-093-3
dc.identifier.officialurlhttp://dx.doi.org/10.1142/9789812702265_0063
dc.identifier.relatedurlhttp://www.worldscientific.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/53488
dc.issue.number831
dc.language.isoeng
dc.page.final584
dc.page.initial577
dc.publisherWorld Scientific Publishing Company
dc.relation.projectIDBFM2003-04147-C02
dc.relation.projectIDFTN2003-08337-C04-04
dc.rights.accessRightsopen access
dc.subject.cdu563
dc.subject.keywordQuantum chaos
dc.subject.keywordNuclei
dc.subject.keywordTime series
dc.subject.ucmFísica (Física)
dc.subject.unesco22 Física
dc.titleChaos and 1/f noise in nuclear spectra
dc.typebook part
dspace.entity.typePublication
relation.isAuthorOfPublication53fed635-944b-485a-b13a-ea8f9355b7aa
relation.isAuthorOfPublication.latestForDiscovery53fed635-944b-485a-b13a-ea8f9355b7aa
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