Europhys. Lett.
Volume 76, Number 6, December 2006
Page(s) 1043 - 1049
Section General
Published online 24 November 2006
Europhys. Lett., 76 (6), pp. 1043-1049 (2006)
DOI: 10.1209/epl/i2006-10392-1

Power spectrum of the fluctuation of the spectral staircase function

Boon Leong Lan1, Jin Aun Ng2 and M. S. Santhanam3

1  School of Engineering, Monash University - Selangor, Malaysia
2  School of Physics, University of Sydney - Sydney, Australia
3  Max Planck Institute for the Physics of Complex Systems - Dresden, Germany

received 9 August 2006; accepted 23 October 2006
published online 24 November 2006

The one-sided power spectrum P(f) of the fluctuation Nfluc (E) and $N_{fluc}(\varepsilon)$ of the spectral staircase function, for respectively the original and unfolded spectrum, from its smooth average part is numerically estimated for Poisson spectrum and spectra of three Gaussian-random matrices: real symmetric, complex Hermitian, and quaternion-real Hermitian. We found that the power spectrum of Nfluc (E) and $N_{fluc}(\varepsilon)$ is a/f2 (brown) for Poisson spectrum but c/(1+ df2) (Lorentzian) for all three random matrix spectra. This result and the Berry-Tabor and Bohigas-Giannoni-Schmit conjectures imply the following conjecture: the power spectrum of Nfluc (E) and $N_{fluc}(\varepsilon)$ is brown for classically integrable systems but Lorentzian for classically chaotic systems. Numerical evidence in support of this conjecture is presented.

05.45.Mt - Quantum chaos; semiclassical methods.
05.45.Tp - Time series analysis.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

© EDP Sciences 2006