RT Journal Article
T1 Correlation structure of the δ_(n) statistic for chaotic quantum systems
A1 Relaño Pérez, Armando
A1 Retamosa Granado, Joaquín
A1 Faleiro, E.
A1 Gómez Gómez, José María
AB The existence of a formal analogy between quantum energy spectra and discrete time series has been recently pointed out. When the energy level fluctuations are described by means of the δ_(n) statistic, it is found that chaotic quantum systems are characterized by 1/f noise, while regular systems are characterized by 1/f(2). In order to investigate the correlation structure of the δ_(n) statistic, we study the qth-order height-height correlation function C-q(tau), which measures the momentum of order q, i.e., the average qth power of the signal change after a time delay tau. It is shown that this function has a logarithmic behavior for the spectra of chaotic quantum systems, modeled by means of random matrix theory. On the other hand, since the power spectrum of chaotic energy spectra considered as time series exhibit 1/f noise, we investigate whether the qth-order height-height correlation function of other time series with 1/f noise exhibits the same properties. A time series of this kind can be generated as a linear combination of cosine functions with arbitrary phases. We find that the logarithmic behavior arises with great accuracy for time series generated with random phases.
PB American Physical Society
SN 1539-3755
YR 2005
FD 2005-12
LK https://hdl.handle.net/20.500.14352/51282
UL https://hdl.handle.net/20.500.14352/51282
LA eng
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.
NO Spanish Government
DS Docta Complutense
RD 17 abr 2025