## Abstract

Spectral property and Lyapunov exponent of electronic wave function (L-exponent) in a modified Bernoulli system with inverse-power-law structural correlation, is studied in detail numerically and theoretically. By changing the value of the bifurcation parameter B specifying a strength of the correlation in the interval (1, ∞), two transitions (a transition around B = 3/2 and another one at B = 2) appear. For the case 3/2 ≤ B <2 of long-range structural correlation, two peaks appear and compete in the distribution function of L-exponent of finite system and the distribution does not obey the central-limit theorem. At the critical point B = 2 (and also for B>2), Lexponent in infinite system vanishes with probability 1.

Original language | English |
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Pages (from-to) | 2295-2304 |

Number of pages | 10 |

Journal | Journal of the Physical Society of Japan |

Volume | 60 |

Issue number | 7 |

Publication status | Published - 1991 Jul |

## Keywords

- Central-limit theorem
- Critical
- Inverse-power law
- Large deviation
- Long-range correlation
- Lyapunov exponent
- Modified Bernoulli
- Renewal process
- Slow convergence
- Spectrum

## ASJC Scopus subject areas

- General Physics and Astronomy