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Power spectrum characterization of the continuous gaussian ensemble
- Source :
- Physical Review E-Statistical Nonlinear and Soft Matter Physics-, ISSN 1539-3755, 2008-03, Vol. 77, No. 3, E-Prints Complutense. Archivo Institucional de la UCM, instname, Archivo Digital UPM, Universidad Politécnica de Madrid, Digital.CSIC. Repositorio Institucional del CSIC, E-Prints Complutense: Archivo Institucional de la UCM, Universidad Complutense de Madrid
- Publication Year :
- 2008
- Publisher :
- E.U.I.T. Industrial (UPM), 2008.
-
Abstract
- 11 pages, 3 figures.-- PACS nrs.: 05.45.Mt; 02.10.Yn; 24.60.-k.-- PMID: 18517325 [PubMed].<br />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.<br />This work was supported in part by Spanish Government Grants Nos. FIS2006-12783-C03-01 and FIS2006-12783-C03-02 and by Comunidad de Madrid–CSIC Grant No. 200650M012. A.R. was supported by the Spanish program "Juan de la Cierva".
- Subjects :
- [PACS] Quantum chaos
semiclassical methods
Level repulsion
Gaussian
Gaussian processes
Matrix algebra
01 natural sciences
Power law
Noise (electronics)
010305 fluids & plasmas
[PACS] Statistical theory and fluctuations in nuclei
symbols.namesake
Matrix (mathematics)
Quantum mechanics
0103 physical sciences
Fluctuations
010306 general physics
Gaussian process
Physics
[PACS] Matrix theory
1/f noise
Termodinámica
Random processes
Spectral density
Física
Function (mathematics)
Minería
symbols
Numerical analysis
Subjects
Details
- Language :
- Spanish; Castilian
- Database :
- OpenAIRE
- Journal :
- Physical Review E-Statistical Nonlinear and Soft Matter Physics-, ISSN 1539-3755, 2008-03, Vol. 77, No. 3, E-Prints Complutense. Archivo Institucional de la UCM, instname, Archivo Digital UPM, Universidad Politécnica de Madrid, Digital.CSIC. Repositorio Institucional del CSIC, E-Prints Complutense: Archivo Institucional de la UCM, Universidad Complutense de Madrid
- Accession number :
- edsair.doi.dedup.....5998e37856ce6403c6c9220c99deaa5c