Power spectrum characterization of the continuous gaussian ensemble

Relaño Pérez, Armando; Muñoz Muñoz, Laura; Faleiro Usanos, Eduardo y Molina, R.A. (2008). Power spectrum characterization of the continuous gaussian ensemble. "Physical Review E- Statistical Nonlinear and Soft Matter Physics-", v. 77 (n. 3); pp.. ISSN 1539-3755. https://doi.org/10.1103/PhysRevE.77.031103.

Descripción

Título: Power spectrum characterization of the continuous gaussian ensemble
Autor/es:
  • Relaño Pérez, Armando
  • Muñoz Muñoz, Laura
  • Faleiro Usanos, Eduardo
  • Molina, R.A.
Tipo de Documento: Artículo
Título de Revista/Publicación: Physical Review E- Statistical Nonlinear and Soft Matter Physics-
Fecha: Marzo 2008
Volumen: 77
Materias:
Escuela: E.U.I.T. Industrial (UPM) [antigua denominación]
Departamento: Física Aplicada [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

The continuous Gaussian ensemble, also known as the ν-Gaussian or ν-Hermite ensemble, is a natural extension of the classical Gaussian ensembles of real (ν=1), complex (ν=2), or quaternion (ν=4) matrices, where ν 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, Pkδ̅ , 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 Pkδ̅ ∝1/k at ν=1 to Pkδ̅ ∝1/k2 at ν=0. Relevantly, the transition is not homogeneous with a 1/fα noise at all scales, but heterogeneous with coexisting 1/f and 1/f2 noises. There exists a critical frequency kc∝ν that separates both behaviors: below kc, Pkδ̅ follows a 1/f power law, while beyond kc, it transits abruptly to a 1/f2 power law. For ν>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 105

Más información

ID de Registro: 2429
Identificador DC: http://oa.upm.es/2429/
Identificador OAI: oai:oa.upm.es:2429
Identificador DOI: 10.1103/PhysRevE.77.031103
URL Oficial: http://pre.aps.org/toc/PRE/v77/i3
Depositado por: Memoria Investigacion
Depositado el: 26 Feb 2010 10:13
Ultima Modificación: 20 Abr 2016 12:07
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