Power spectrum characterization of the continuous gaussian ensemble

Relaño Pérez, Armando and Muñoz Muñoz, Laura and Faleiro Usanos, Eduardo and 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.

Description

Title: Power spectrum characterization of the continuous gaussian ensemble
Author/s:
  • Relaño Pérez, Armando
  • Muñoz Muñoz, Laura
  • Faleiro Usanos, Eduardo
  • Molina, R.A.
Item Type: Article
Título de Revista/Publicación: Physical Review E- Statistical Nonlinear and Soft Matter Physics-
Date: March 2008
ISSN: 1539-3755
Volume: 77
Subjects:
Faculty: E.U.I.T. Industrial (UPM)
Department: Física Aplicada [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (344kB) | Preview

Abstract

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

More information

Item ID: 2429
DC Identifier: http://oa.upm.es/2429/
OAI Identifier: oai:oa.upm.es:2429
DOI: 10.1103/PhysRevE.77.031103
Official URL: http://pre.aps.org/toc/PRE/v77/i3
Deposited by: Memoria Investigacion
Deposited on: 26 Feb 2010 10:13
Last Modified: 20 Apr 2016 12:07
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM