### Abstract

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 language | English |
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Pages (from-to) | 1043-1049 |

Number of pages | 7 |

Journal | EPL |

Volume | 76 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2006 |

## Cite this

Lan, B. L. (2006). Power spectrum of the fluctuation of the spectral staircase function.

*EPL*,*76*(6), 1043-1049. https://doi.org/10.1209/epl/i2006-10392-1