Relaño Pérez, ArmandoGómez Gómez, José MaríaRetamosa Granado, JoaquínFaleiro, E.Salasnich, L.Vranicar, M.Robnik, M.2023-06-202023-06-202005-03-04[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).0031-900710.1103/PhysRevLett.94.084101https://hdl.handle.net/20.500.14352/51285©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.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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevLett.94.084101http://journals.aps.org/open access536Energy-Level StatisticsAnalytic BoundariesClassical DynamicsTransition RegionPhase-SpaceBilliardsIntegrabilityFamilyChaosTermodinámica2213 Termodinámica