Publication: 1/f noise and very high spectral rigidity
Loading...
Official URL
Full text at PDC
Publication Date
2006-02
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
It was recently pointed out that the spectral fluctuations of quantum systems are formally analogous to discrete time series, and therefore their structure can be characterized by the power spectrum of the signal. Moreover, it is found that the power spectrum of chaotic spectra displays a 1/f behavior, while that of regular systems follows a 1/f(2) law. This analogy provides a link between the concepts of spectral rigidity and antipersistence. Trying to get a deeper understanding of this relationship, we have studied the correlation structure of spectra with high spectral rigidity. Using an appropriate family of random Hamiltonians, we increase the spectral rigidity up to hindering completely the spectral fluctuations. Analyzing the long range correlation structure a neat power law 1/f has been found for all the spectra, along the whole process. Therefore, 1/f noise is the characteristic fingerprint of a transition that, preserving the scale-free correlation structure, hinders completely the fluctuations of the spectrum.
Description
©2006 The American Physical Society. This work is supported in part by Spanish Government Grants No. BFM2003-04147 and No. FTN2003-08337-C04-04.
UCM subjects
Unesco subjects
Keywords
Citation
[1] M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 (1977).
[2] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
[3] H. J. Stöckmann, Quantum Chaos (Cambridge University Press, Cambridge, U.K., 1999).
[4] T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299, 189 (1998).
[5] A. Relaño, J. M. G. Gómez, R. A. Molina, J. Retamosa, and E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002).
[6] E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño, and J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004).
[7] J. M. G. Gómez, A. Relaño, J. Retamosa, E. Faleiro, M. Vranicar, and M. Robnik, Phys. Rev. Lett. 94, 084101 (2005); M. S. Santhanam and J. N. Bandyopadhyay, Phys. Rev. Lett. 95, 114101 (2005).
[8] P. Leboeuf, A. G. Monastra, and O. Bohigas, Regular Chaotic Dyn. 6, 205 (2001).
[9] M. Krbalek, P. Seba, and P. Wagner, Phys. Rev. E 64, 066119 (2001).
[10] R. A. Molina, A. P. Zuker, A. Relaño, and J. Retamosa, Phys. Rev. C 71, 064317 (2005).
[11] M. L. Mehta, Random Matrices (Academic, New York, 1991).
[13] J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford University Press, Oxford, 1996).
[14] F. M. Izrailev, Phys. Lett. A 134, 13 (1988).
[15] R. Scharf and F. M. Izrailev, J. Phys. A 23, 963 (1990).
[16] F. J. Dyson, J. Math. Phys. 3, 140 (1962); 3, 157 (1962).