Power spectrum of the fluctuation of the spectral staircase function

Boon Leong Lan

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    3 Citations (Scopus)


    The one-sided power spectrum P(f) of the fluctuation N-fluc(E) and N-fluc(epsilon) of the spectral staircase function, for respectively the original mid unfolded spectrum, from its smooth average part is numerically estimated for Poisson spectrum and spectra of till-cc Gaussian-random matrices: real symmetric, complex Hermitian, and quaternion-real Hermitian. We found that the power spectrum of N-fluc(E) and N-fluc(epsilon) is a/f(2) (brown) for Poisson spectrum bnt c/(1 + df(2)) (Lorentzian) for all three random matrix spectra. This result and the Berry-Tabor and Bohigas-Giannoni-Schmit conjectures imply the following conjecture: the power spectrum of N-fluc(E) mid N-fluc(epsilon) is brown for classically integrable systems but Lorentzian for classically chaotic systems. Numerical evidence in support, of this conjecture is presented.
    Original languageEnglish
    Pages (from-to)1043-1049
    Number of pages7
    Issue number6
    Publication statusPublished - Dec 2006

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