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Relaño Pérez, Armando and Muñoz, L. and Retamosa Granado, Joaquín and Faleiro, E. and Molina, R. A. (2008) Powerspectrum characterization of the continuous Gaussian ensemble. Physical Review E, 77 (3). ISSN 15393755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.77.031103
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http://journals.aps.org/  Publisher 
Abstract
The continuous Gaussian ensemble, also known as the nuGaussian or nuHermite ensemble, is a natural extension of the classical Gaussian ensembles of real (nu= 1), complex (nu= 2), or quaternion (nu=4) matrices, where nu 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 terracewidth 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 longrange spectral correlations of this ensemble by means of the delta(n) statistic. We derive an analytical expression for the average power spectrum of this statistic, <(P(k)(delta))over bar>, based on approximated forms for the twopoint cluster function and the spectral form factor. We find that the power spectrum of delta(n) evolves from <(P(k)(delta))over bar> proportional to 1/ k at nu= 1 to <(P(k)(delta))over bar> proportional to 1/ k(2) at nu= 0. Relevantly, the transition is not homogeneous with a 1/ f alpha noise at all scales, but heterogeneous with coexisting 1/ f and 1/ f(2) noises. There exists a critical frequency k(c)proportional to nu that separates both behaviors: below k(c), <(P(k)(delta))over bar> follows a 1/f power law, while beyond kc, it transits abruptly to a 1/ f(2) power law. For nu>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).
Item Type:  Article 

Additional Information:  © 2008 The American Physical Society. This work was supported in part by Spanish Government Grants Nos. FIS200612783C0301 and FIS200612783C0302 and by Comunidad de Madrid–CSIC Grant No. 200650M012. A.R. was supported by the Spanish program “Juan de la Cierva”. 
Uncontrolled Keywords:  ManyParticle Spectra, One Dimension, Statistical Properties, RandomMatrix, Ground State, Body Problem, Eigenvalues, Hermite 
Subjects:  Sciences > Physics > Thermodynamics 
ID Code:  27625 
Deposited On:  17 Dec 2014 12:14 
Last Modified:  17 Dec 2014 12:14 
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