RT Journal Article
T1 1/ƒ^(α) noise in spectral fluctuations of quantum systems
A1 Relaño Pérez, Armando
A1 Gómez Gómez, José María
A1 Retamosa Granado, Joaquín
A1 Faleiro, E.
A1 Salasnich, L.
A1 Vranicar, M.
A1 Robnik, M.
AB The power law 1/ƒ^(α) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/ƒ^(α) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.
PB American Physical Society
SN 0031-9007
YR 2005
FD 2005-03-04
LK https://hdl.handle.net/20.500.14352/51285
UL https://hdl.handle.net/20.500.14352/51285
LA eng
NO [1] B. B. Mandelbrot, Multifractals and 1/f Noise (Springer, New York, 1999).[2] A. Relaño, J. M. G. Gómez, R. A. Molina, J. Retamosa, and E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002).[3] M. Robnik, report, CAMTP, December 2003 (to be published).[4] H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, England, 1999).[5] M.V. Berry and M. Tabor, Proc. R. Soc. London A 356, 375 (1977).[6] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).[7] G. Casati, F. Valz-Gris, and I. Guarneri, Lett. Nuovo Cimento 28, 279 (1980).[8] M. Robnik, J. Phys. A 16, 3971 (1983).[9] G. Veble, U. Kuhl, M. Robnik, H.-J. Stöckmann, J. Liu, and M. Barth, Prog. Theor. Phys. Suppl. 139, 283 (2000).[10] M. Robnik, J. Phys. A 17, 1049 (1984); T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994); M. Robnik and T. Prosen, J. Phys. A 30, 8787 (1997).[11] T. Prosen and M. Robnik, J. Phys. A 26, 2371 (1993).[12] R. Markarian, Nonlinearity 6, 819 (1993).[13] M. L. Mehta, Random Matrices, (Academic, New York, 1991).[14] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981).[15] I. C. Percival, J. Phys. B 6, L229 (1973).[16] M.V. Berry, Philos. Trans. R. Soc. London A 287, 237 (1977); M.V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984); M. Robnik, in Atomic Spectra and Collisions in External Fields, edited by K. T. Taylor et al. (Plenum, New York, 1988) p. 265; M. Robnik, Nonlinear Phenomena in Complex Systems (Minsk) 1, No. 1, 1 (1998); M. Robnik, J. Phys. Soc. Jpn., Suppl. C 72, 81 (2003).[17] T. Prosen and M. Robnik, J. Phys. A 27, 8059 (1994); T. Prosen, J. Phys. A 31, 7023 (1998); T. Prosen and M. Robnik, J. Phys. A 32, 1863 (1999); J. Malovrh and T. Prosen, J. Phys. A 35, 2483 (2002).[18] E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño, and J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004).
NO ©2005 The American Physical Society. This work is supported in part by Spanish Government Grant Nos. BFM2003-04147-C02 and FTN2003-08337-C04-04. This work is also supported by the Ministry of Education, Science and Sports of the Republic of Slovenia.
NO Spanish Government
NO Ministry of Education, Science and Sports of the Republic of Slovenia
DS Docta Complutense
RD 6 may 2024