### 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 |
---|---|

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 |

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### 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

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*60*(7), 2295-2304.

**A new class of disordered systems a modified Bernoulli system with long range structural correlation.** / Goda, Masaki; Yamada, Hiroaki; Aizawa, Yoji; Kurumi, Kaoru; Shudo, Akira; Kubo, Haruhiko.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 60, no. 7, pp. 2295-2304.

}

TY - JOUR

T1 - A new class of disordered systems a modified Bernoulli system with long range structural correlation

AU - Goda, Masaki

AU - Yamada, Hiroaki

AU - Aizawa, Yoji

AU - Kurumi, Kaoru

AU - Shudo, Akira

AU - Kubo, Haruhiko

PY - 1991/7

Y1 - 1991/7

N2 - 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.

AB - 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.

KW - Central-limit theorem

KW - Critical

KW - Inverse-power law

KW - Large deviation

KW - Long-range correlation

KW - Lyapunov exponent

KW - Modified Bernoulli

KW - Renewal process

KW - Slow convergence

KW - Spectrum

UR - http://www.scopus.com/inward/record.url?scp=0005534534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005534534&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0005534534

VL - 60

SP - 2295

EP - 2304

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 7

ER -