1f noise and very high spectral rigidity

A. Relaño, J. Retamosa, E. Faleiro, R. A. Molina, and A. P. Zuker
Phys. Rev. E 73, 026204 – Published 7 February 2006

Abstract

It was recently pointed out that the spectral fluctuations of quantum systems are formally analogous to discrete time series, and therefore their structure can be characterized by the power spectrum of the signal. Moreover, it is found that the power spectrum of chaotic spectra displays a 1f behavior, while that of regular systems follows a 1f2 law. This analogy provides a link between the concepts of spectral rigidity and antipersistence. Trying to get a deeper understanding of this relationship, we have studied the correlation structure of spectra with high spectral rigidity. Using an appropriate family of random Hamiltonians, we increase the spectral rigidity up to hindering completely the spectral fluctuations. Analyzing the long range correlation structure a neat power law 1f has been found for all the spectra, along the whole process. Therefore, 1f noise is the characteristic fingerprint of a transition that, preserving the scale-free correlation structure, hinders completely the fluctuations of the spectrum.

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  • Received 9 August 2005

DOI:https://doi.org/10.1103/PhysRevE.73.026204

©2006 American Physical Society

Authors & Affiliations

A. Relaño1, J. Retamosa1, E. Faleiro2, R. A. Molina3, and A. P. Zuker4

  • 1Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, 28010 Madrid, Spain
  • 2Departamento de Física Aplicada, EUIT Industrial, Universidad Politécnica de Madrid, 28012 Madrid, Spain
  • 3Max-Planck-institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187, Dresden, Germany
  • 4IReS, Bâtiment 27, IN2P3-CNRS/Université Louis Pasteur, Boite Postale 28, F-67037 Strasbourg Cedex 2, France

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Vol. 73, Iss. 2 — February 2006

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