RT Journal Article T1 Perspectives on 1/ƒ noise in quantum chaos A1 Relaño Pérez, Armando A1 Molina, R. A. A1 Retamosa Granado, Joaquín A1 Muñoz, L. A1 Faleiro, E. A1 Gómez Gómez, José María AB The power spectrum of the δ_(n) statistic of quantum spectra presents 1/ƒ^(α) noise. For chaotic systems α = 1 while for regular systems α = 2. Although the transition from regularity to chaos is non universal, for a wide variety of systems with a mixed phase space the value of α is intermediate between 1 and 2 and can be related to the fraction of regular or chaotic orbits in the total phase space. This statistic can be a very useful tool for the analysis of experimental spectra, specially in the case of missing levels or spectral sequences with mixed symmetries. PB IOP Publishing Ltd SN 1742-6588 YR 2010 FD 2010 LK https://hdl.handle.net/20.500.14352/44419 UL https://hdl.handle.net/20.500.14352/44419 LA eng NO [1] Berry M V and Tabor M 1977 Proc. R. Soc. London A 356 375[2] Bohigas O, Giannoni M J and Schmidt C 1984 Phys. Rev. Lett. 52 1[3] Heusler S, Müller S, Altland A, Braun P and Haake F 2007 Phys. Rev. Lett. 98 044103[4] Relaño A, Gómez J M G, Molina R A, Retamosa J and Faleiro E 2002 Phys. Rev. Lett. 89 244102[5] Mandelbrot B B 1999 Multifractals and 1/f noise Springer New York[6] Greis N P and Greenside H S 1991 Phys. Rev. A 44 2730[7] Relaño A, Molina R A and Retamosa J 2004 Phys. Rev. E 70 017201[8] Faleiro E, Gómez J M G, Muñoz L, Molina R A, Relaño A and Retamosa J 2004 Phys. Rev. Lett. 93 244101[9] French J B, Kota V K B, Pandey A and Tomsovic S 1988 Ann. Phys. (N.Y.) 181 198[10] Smith J O 2003 Mathematics of the Discrete Fourier Transform (DFT) ISBN 0 9745607-0-7 [http://ccrmawww. standford.edu/jos/mdft/][11] Faleiro E, Kuhl U, Molina R A, Muñoz L, Relaño A and Retamosa J 2006 Phys. Lett. A 358 251[12] Molina R A and Muñoz L et al 2007 Phys. Lett. B 644 25[13] Agvaanluvsan U, Mitchell G E, Shriner Jr. J F and Pato M P 2003 Nucl. Instr. Meth. A 498 459[14] Bohigas O and Pato M P 2006 Phys. Rev. E 74 036212[15] García García A M 2006 Phys. Rev. E 73, 026213[16] Gómez J M G, Relaño A, Retamosa J, Faleiro E, Salasnich L, Vranicar M and Robnik M 2005 Phys. Rev. Lett. 94 114101[17] Santhanam M S and Bandyopadhayay J N 2005 Phys. Rev. Lett. 95 114101[18] Robnik M 2006 Int. J. Bifurcation Chaos Appl. Sci. Eng. 16 1849[19] Male C, Le Caër G and Delannay D 2007 Phys. Rev. E 76 042101[20] Tomsovic S, Ullmo D 1994 Phys. Rev. E 50 145[21] Relaño A 2008 Phys. Rev. Lett. 100 224101 NO © 2010 IOP Publishing Ltd. Symposium on Nuclear Physics (33rd. 2010. Morelos, México). This research has been supported in part by Spanish Government grant No. FIS2009-07277 and No. FIS2006-12783-C03-02, CSPD-2007 00042-Ingenio2010, and by the Universidad Complutense de Madrid grant UCM-910059. A.R. is supported by the CPAN Consolider program. NO Spanish Government NO Universidad Complutense de Madrid NO CPAN-Consolider program DS Docta Complutense RD 18 jul 2024