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Please use this identifier to cite or link to this item: http://hdl.handle.net/10261/11050
Title: Power-spectrum characterization of the continuous Gaussian ensemble
Authors: Relaño, Armando; Muñoz, L.; Retamosa, J.; Faleiro, E.; Molina, Rafael A.
Keywords: 1/f noise
Gaussian processes
Matrix algebra
Numerical analysis
Random processes
[PACS] Quantum chaos; semiclassical methods
[PACS] Matrix theory
[PACS] Statistical theory and fluctuations in nuclei
Issue Date: 4-Mar-2008
Publisher: American Physical Society
Citation: Physical Review E 77(3): 031103 (2008)
Abstract: The continuous Gaussian ensemble, also known as the v-Gaussian or v-Hermite ensemble, is a natural extension of the classical Gaussian ensembles of real (v=1), complex (v=2), or quaternion (v=4) matrices, where v is allowed to take any positive value. From a physical point of view, this ensemble may be useful to describe transitions between different symmetries or to describe the terrace-width distributions of vicinal surfaces. Moreover, its simple form allows one to speed up and increase the efficiency of numerical simulations dealing with large matrix dimensions. We analyze the long-range spectral correlations of this ensemble by means of the δn statistic. We derive an analytical expression for the average power spectrum of this statistic, [overline Pk[sup δ]], based on approximated forms for the two-point cluster function and the spectral form factor. We find that the power spectrum of δn evolves from [overline Pk[sup δ]] proportional to 1/k at v=1 to [overline Pk[sup δ]] proportional to 1/k^2 at v=0. Relevantly, the transition is not homogeneous with a 1/fα noise at all scales, but heterogeneous with coexisting 1/f and 1/f^2 noises. There exists a critical frequency kc proportional to v that separates both behaviors: below kc, [overline Pk[sup δ]] follows a 1/f power law, while beyond kc, it transits abruptly to a 1/f^2 power law. For v>1 the 1/f noise dominates through the whole frequency range, unveiling that the 1/f correlation structure remains constant as we increase the level repulsion and reduce to zero the amplitude of the spectral fluctuations. All these results are confirmed by stringent numerical calculations involving matrices with dimensions up to 10^5.
Description: 11 pages, 3 figures.-- PACS nrs.: 05.45.Mt; 02.10.Yn; 24.60.-k.-- PMID: 18517325 [PubMed].
Publisher version (URL): http://dx.doi.org/10.1103/PhysRevE.77.031103
URI: http://hdl.handle.net/10261/11050
DOI: 10.1103/PhysRevE.77.031103
ISSN: 1539-3755
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