Issue |
Europhys. Lett.
Volume 76, Number 6, December 2006
|
|
---|---|---|
Page(s) | 1043 - 1049 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2006-10392-1 | |
Published online | 24 November 2006 |
Power spectrum of the fluctuation of the spectral staircase function
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
The one-sided power spectrum of the fluctuation
and
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
and
is
(brown) for Poisson spectrum but
(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
and
is brown for classically integrable systems but Lorentzian for classically chaotic systems. Numerical evidence in support of
this conjecture is presented.
PACS: 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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.